5.5 Roots Of Real Numbers
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Date____________________ HW Honors p248 (16-56) evens Regular p248(16-24) evens (28-50) evens
Notes Section 5.5 – Roots of Real Numbers The symbol
indicates an nth root
n
n
50
SQUARE ROOTS When we raise a number to the second power, we say that we have squared the number. Sometimes we may need to find the number that was squared. We call this process finding a square root of a number. For example: 5 is a square root of 25 because 52 = 5 5 = 25 -5 is a square root of 25 because (-5)2 = (-5) ( -5) = 25
•
•
The number -4 does not have a real number square root because there is no real number b such that b2=-4 SQUARE ROOTS Every positive real number has two real number square roots The number 0 has just one square root, 0 itself. Negative numbers do not have real number square roots. Directions: Simplify EX 1.
ST1.
a.) ± 25 x 4
a.) ± 25 x 4
_______________
_______________
b.) −
(y
2
+2
)
8
_______________ c.)
5
b.) −
(y
3
+5
)
4
_______________ c.)
32 x 15 y 20
5
243 x 10 y 15
_______________
_______________
d.)
d.)
−9
_______________
−4
_______________
Directions : Use a calculator to approximate each value to THREE DECIMAL PLACES
EX2.
ST2.
a.)
77
_______________
a.) - 147
_______________
b.) -
3
_______________
b.)
602
_______________
c.)
48
_______________
c.)
− 480
_______________
4
19
4
3
SIMPLIFYING USING ABSOLUTE VALUES When you find the nth root of an even power and the result is an odd power you must take the absolute value to ensure a positive answer. (ONLY WORKS WITH VARIABLES) EX3. 1.)
8
x8
_______________
2.)
4
81 ( a +1)12
_______________
3.)
4 x 2 + 4 x +1
_______________
4.)
64 x 6
_______________
ST3. 1.)
2
16 x 6
_______________
2.)
4
16 ( x + 2) 4
_______________
3.)
x 2 + 4x + 4
_______________
4.)
49 x 2
_______________
Notes Section 5.5 – Roots of Real Numbers The symbol
indicates an nth root
n
n
50
SQUARE ROOTS When we raise a number to the second power, we say that we have squared the number. Sometimes we may need to find the number that was squared. We call this process finding a square root of a number. For example: 5 is a square root of 25 because 52 = 5 5 = 25 -5 is a square root of 25 because (-5)2 = (-5) ( -5) = 25
•
•
The number -4 does not have a real number square root because there is no real number b such that b2=-4 SQUARE ROOTS Every positive real number has two real number square roots The number 0 has just one square root, 0 itself. Negative numbers do not have real number square roots. Directions: Simplify EX 1.
ST1.
a.) ± 25 x 4
a.) ± 25 x 4
_______________
_______________
b.) −
(y
2
+2
)
8
_______________ c.)
5
b.) −
(y
3
+5
)
4
_______________ c.)
32 x 15 y 20
5
243 x 10 y 15
_______________
_______________
d.)
d.)
−9
_______________
−4
_______________
Directions : Use a calculator to approximate each value to THREE DECIMAL PLACES
EX2.
ST2.
a.)
77
_______________
a.) - 147
_______________
b.) -
3
_______________
b.)
602
_______________
c.)
48
_______________
c.)
− 480
_______________
4
19
4
3
SIMPLIFYING USING ABSOLUTE VALUES When you find the nth root of an even power and the result is an odd power you must take the absolute value to ensure a positive answer. (ONLY WORKS WITH VARIABLES) EX3. 1.)
8
x8
_______________
2.)
4
81 ( a +1)12
_______________
3.)
4 x 2 + 4 x +1
_______________
4.)
64 x 6
_______________
ST3. 1.)
2
16 x 6
_______________
2.)
4
16 ( x + 2) 4
_______________
3.)
x 2 + 4x + 4
_______________
4.)
49 x 2
_______________
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