27 May Basic Maths
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MATHS MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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What is the square root of .0009? • After decimal, we take numbers in pairs of two for taking square root, the last pair is 09 or 9 only. • Square root of 9 is 3. there are four digits after zero, so make it .03 Ans.
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What is the least number of 4 digits, which is a perfect square? • The lease number of four digits is 1000, but it is not perfect square. Square root of 1000 is 31.6, so next number is 32. Square of 32 is: 1024, so answer is 1024. • Calculating square of 1000: take 1000 in a pair of two digits each – so you have 10. divide 10 by 3*3 = remainder is 1. now you have 100 (bring 00 to make it 100), now divide it by 61*1 = 61 (you cant divide it by 2, because 62*2 = 124 – more than 100), by this you come to know that square of 32 is your answer.
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What is the greatest number of 4 digits, which is perfect square? • Greatest number of 4 digits will be just less than least number of 5 digits. Least no. of 5 digits is 10000 – whose square root is 100. So deducting one from 100, we get 99. Square of 99 is 9801 Ans.
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What must be multiplied to 352 to make it a perfect square? • Factors of 352 are:2*2*2*2*2*11 • Now here 2 has come 5 times – but it should be 6 times. • 11 has come once, but it should come twice. • Therefore, multiply it by 2*11 – so we have to multiply it by 22 to make it square (2 will be 6 times and 11 with be 2 times) . Ans.
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What must be divided from 352 to make it a perfect square? • Factors of 352 are:2*2*2*2*2*11 • Now here 2 has come 5 times – but it should be 4 times. • 11 has come once, but it should not come (or come in square). Therefore, divide it by 2*11 – so we have to divide it by 22 to make it square (2 will be 4 times) . Ans.
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What must be added to 352 to make it a perfect square? • Make it pairs – last pair is 52, first pair is 03. divide 03 by 1, remainder is 2, now we have 252, now if we divide by 8, we get 28*8= 224, if we divide by 9 we get 29*9, = 261. therefore we deduct 252 from 261, we get 9, so we have to add 9 in it to make it perfect square. Ans. www.afterschoool.tk
What must be subtracted from 352 to make it a perfect square? • Make it pairs – last pair is 52, first pair is 03. divide 03 by 1, remainder is 2, now we have 252, now if we divide by 8, we get 28*8= 224, if we divide by 9 we get 29*9, = 261. therefore we deduct224 from 252, we get 28, so we have to subtract 28 from it to make it perfect square. Ans.
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What is the smallest number to be subtracted from 549162 to make it perfect square? • Make pairs of 54,91 and 62, divide 54 by 7*7 – remainder is 5, now we have 591, divide it by 144*4 = 576 remainder is 15, now we have 1562. Divide this by 1481*1 = 1481, remainder is 81, so we have to subtract 81 to make it perfect square Ans. www.afterschoool.tk
What is the square root of .00009? • .003 ans. • Sorry – it is wrong answer • Let us make pairs of two digits from decimals, since we have five digits, make it 6 digits - .000090, now we have three pairs. we have 00, 00, 90. Square root of 00 is 0, and square root of 90 is 9.48, so square root of this number is .00948 Ans.
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Smallest perfect square divisible by 8, 15,18 and 25 is ? The factors of 8 =2*2*2 Factors of 15 = 3*5 Factors of 18 = 2*3*3 Factors of 25 = 5*5 Maximum power of 5 is 2, so take 5*5, maximum power of 2 is 3, so make it 4, so take: 2^4, maximum power of 3 is 2, so take 3^2. • So take each of these factors in multiple of 2 we have : 2*2*2*2*3*3*5*5 = 3600 ans. • • • • •
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Smallest perfect cube divisible by 8, 15,18 and 25 is ? The factors of 8 =2*2*2 Factors of 15 = 3*5 Factors of 18 = 2*3*3 Factors of 25 = 5*5 Maximum power of 5 is 2, so make it 3 take 5^3, maximum power of 2 is 3, so take: 2^3, maximum power of 3 is 2, so make it 3 and take 3^3. • So take each of these factors in multiple of 3 we have : 2*2*2*3*3*3*5*5*5 =27000 ans. • • • • •
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All the students of AFTESCHOOOL stand in the form of a solid square. Some well wishers are also there, but they are not part of square. There are total of 150 persons. How many persons are standing in the first row of square. How many are well wishers, if it is given that number of well wisher is half of no. of the persons in the row?
• The perfect square just less than 150 is 144. So, there must be 12 persons in first row. And there must be 6 well wishers. 6+12*12 gives 150, so this is the answer. www.afterschoool.tk
What is the value of 1/ (9^1/2 +8^1/2 )? • Remember formulae: (x+y) (x-y)= x^2 – y^2 • Step 1: multiply this number by (9^1/2 -8^1/2) /(9^1/2 -8^1/2) • Now the number becomes: • (9^1/2 -8^1/2)/(9-8) • 3-2.828 = .182Ans. www.afterschoool.tk
What is the value of (32^1/2 +48^1/2 )/(12^1/2 +8^1/2 )? Let us make their factors ignoring square roots. 2*2*2*2*2 + 2*2*2*2*3 Divided by 2*2*3 +2*2*2 16 is common in numerator and 4 is common in denominator, so we have 16/4 = 4, take square root of 4 = 2. • Other things are common – so cut them – 1 is left. We have 2*1 = 2 Ans. • • • •
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What do you get from: (.036*.049*.0025)^1/2 / (.016*.0064*.081)^1/2 ? • All these numbers are after decimals. There are 10 digits after decimals – we can cut all decimals, so let us ignore decimals. Now take their square roots. , we have 6*7*5/4*8*9 • We get 35/48. Ans.
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What is the value of (176+2401^1/2 ) ^1/2 ? • First solve 2401 (which is bracket) and get its square root. Its square root is 49. • Now add 49 to 176, we get 225. • Now take square root of 225, we get 15 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • • • • •
www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
What is the square root of .0009? • After decimal, we take numbers in pairs of two for taking square root, the last pair is 09 or 9 only. • Square root of 9 is 3. there are four digits after zero, so make it .03 Ans.
www.afterschoool.tk
What is the least number of 4 digits, which is a perfect square? • The lease number of four digits is 1000, but it is not perfect square. Square root of 1000 is 31.6, so next number is 32. Square of 32 is: 1024, so answer is 1024. • Calculating square of 1000: take 1000 in a pair of two digits each – so you have 10. divide 10 by 3*3 = remainder is 1. now you have 100 (bring 00 to make it 100), now divide it by 61*1 = 61 (you cant divide it by 2, because 62*2 = 124 – more than 100), by this you come to know that square of 32 is your answer.
www.afterschoool.tk
What is the greatest number of 4 digits, which is perfect square? • Greatest number of 4 digits will be just less than least number of 5 digits. Least no. of 5 digits is 10000 – whose square root is 100. So deducting one from 100, we get 99. Square of 99 is 9801 Ans.
www.afterschoool.tk
What must be multiplied to 352 to make it a perfect square? • Factors of 352 are:2*2*2*2*2*11 • Now here 2 has come 5 times – but it should be 6 times. • 11 has come once, but it should come twice. • Therefore, multiply it by 2*11 – so we have to multiply it by 22 to make it square (2 will be 6 times and 11 with be 2 times) . Ans.
www.afterschoool.tk
What must be divided from 352 to make it a perfect square? • Factors of 352 are:2*2*2*2*2*11 • Now here 2 has come 5 times – but it should be 4 times. • 11 has come once, but it should not come (or come in square). Therefore, divide it by 2*11 – so we have to divide it by 22 to make it square (2 will be 4 times) . Ans.
www.afterschoool.tk
What must be added to 352 to make it a perfect square? • Make it pairs – last pair is 52, first pair is 03. divide 03 by 1, remainder is 2, now we have 252, now if we divide by 8, we get 28*8= 224, if we divide by 9 we get 29*9, = 261. therefore we deduct 252 from 261, we get 9, so we have to add 9 in it to make it perfect square. Ans. www.afterschoool.tk
What must be subtracted from 352 to make it a perfect square? • Make it pairs – last pair is 52, first pair is 03. divide 03 by 1, remainder is 2, now we have 252, now if we divide by 8, we get 28*8= 224, if we divide by 9 we get 29*9, = 261. therefore we deduct224 from 252, we get 28, so we have to subtract 28 from it to make it perfect square. Ans.
www.afterschoool.tk
What is the smallest number to be subtracted from 549162 to make it perfect square? • Make pairs of 54,91 and 62, divide 54 by 7*7 – remainder is 5, now we have 591, divide it by 144*4 = 576 remainder is 15, now we have 1562. Divide this by 1481*1 = 1481, remainder is 81, so we have to subtract 81 to make it perfect square Ans. www.afterschoool.tk
What is the square root of .00009? • .003 ans. • Sorry – it is wrong answer • Let us make pairs of two digits from decimals, since we have five digits, make it 6 digits - .000090, now we have three pairs. we have 00, 00, 90. Square root of 00 is 0, and square root of 90 is 9.48, so square root of this number is .00948 Ans.
www.afterschoool.tk
Smallest perfect square divisible by 8, 15,18 and 25 is ? The factors of 8 =2*2*2 Factors of 15 = 3*5 Factors of 18 = 2*3*3 Factors of 25 = 5*5 Maximum power of 5 is 2, so take 5*5, maximum power of 2 is 3, so make it 4, so take: 2^4, maximum power of 3 is 2, so take 3^2. • So take each of these factors in multiple of 2 we have : 2*2*2*2*3*3*5*5 = 3600 ans. • • • • •
www.afterschoool.tk
Smallest perfect cube divisible by 8, 15,18 and 25 is ? The factors of 8 =2*2*2 Factors of 15 = 3*5 Factors of 18 = 2*3*3 Factors of 25 = 5*5 Maximum power of 5 is 2, so make it 3 take 5^3, maximum power of 2 is 3, so take: 2^3, maximum power of 3 is 2, so make it 3 and take 3^3. • So take each of these factors in multiple of 3 we have : 2*2*2*3*3*3*5*5*5 =27000 ans. • • • • •
www.afterschoool.tk
All the students of AFTESCHOOOL stand in the form of a solid square. Some well wishers are also there, but they are not part of square. There are total of 150 persons. How many persons are standing in the first row of square. How many are well wishers, if it is given that number of well wisher is half of no. of the persons in the row?
• The perfect square just less than 150 is 144. So, there must be 12 persons in first row. And there must be 6 well wishers. 6+12*12 gives 150, so this is the answer. www.afterschoool.tk
What is the value of 1/ (9^1/2 +8^1/2 )? • Remember formulae: (x+y) (x-y)= x^2 – y^2 • Step 1: multiply this number by (9^1/2 -8^1/2) /(9^1/2 -8^1/2) • Now the number becomes: • (9^1/2 -8^1/2)/(9-8) • 3-2.828 = .182Ans. www.afterschoool.tk
What is the value of (32^1/2 +48^1/2 )/(12^1/2 +8^1/2 )? Let us make their factors ignoring square roots. 2*2*2*2*2 + 2*2*2*2*3 Divided by 2*2*3 +2*2*2 16 is common in numerator and 4 is common in denominator, so we have 16/4 = 4, take square root of 4 = 2. • Other things are common – so cut them – 1 is left. We have 2*1 = 2 Ans. • • • •
www.afterschoool.tk
What do you get from: (.036*.049*.0025)^1/2 / (.016*.0064*.081)^1/2 ? • All these numbers are after decimals. There are 10 digits after decimals – we can cut all decimals, so let us ignore decimals. Now take their square roots. , we have 6*7*5/4*8*9 • We get 35/48. Ans.
www.afterschoool.tk
What is the value of (176+2401^1/2 ) ^1/2 ? • First solve 2401 (which is bracket) and get its square root. Its square root is 49. • Now add 49 to 176, we get 225. • Now take square root of 225, we get 15 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • • • • •
www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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