11.2a
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11.2A. Simplify and Multiply Square Roots. Squaring a Number . When a number is squared, it is multiplied to itself: . 1. 5. 5. 25. -3. -3. 9. Notice squaring any number always results in a ___________________ number. . positive. Taking the Square Root of a Number - PowerPoint PPT PresentationTRANSCRIPT
11.2A
Simplify and Multiply Square Roots
Squaring a Number When a number is squared, it is multiplied to itself:
21 1 1 __ 25 __ __ ___
2( 3) __ __ ___
1 5 5 25
-3 -3 9Notice squaring any number always results in a ___________________ number. positive
Taking the Square Root of a Number
Just as subtracting is the opposite of
adding and dividing is the opposite of
multiplying, the opposite of squaring is
____________ ______________.square rooting
Ex 1: Find the square roots of the following numbers:
9
1
232
m2
25
3 1
23 m
Not possible!
Ex 2: Find the following: (Think of the negative sign in front as just being negative one multiplied to the positive root.)
232
25 –5
–23
m2 –m
–x
x22y3
Factor tree inside radicalCircle any pairsMultiply pairs w/ # in frontMultiply loners back inside
Ex 4: Simplify
a) 205 4
2 2
= 2 5
2 36
6 6
72
23 23
b)= 6 2
Ex 4: Simplify
c) 250x2 25
5 5
x x
= 5 2x
Ex 4: Simplify
d) 624x2 12
2 6
2 3
x x x x x x
= 2 6x3
Ex 4: Simplify
e) 22 18x
2 9
3 3
x x
= 6 2x
Ex 4: Simplify
f) 165 12y
3 4
2 2
= 10 3y8
10 10
107 100x =g)
70x5
h)
5 8
4 2
83 40y
2 2
= 6 10y4
Multiply #s in frontMultiply #s insideFactor tree and simplify
2 35
5 49
7 7
= 35
20x2
5 4
2 2
= 2 5x
240y10
24 10
6 4
3 2 2 22 5
= 4 15y5
6 5t6 = 6 5t3
14 12k8
4 3
2 2
= 28 3k4
Divide exponent by 2Leave remainder 1 inside
x x x
= xx
= 4 pp2
6 4
3 2 2 2
= 2 6kk9
8 4
4 22 2
22
= 20 2ww7
6 6
= 6 pp3
7 42 2
= 2 7xx7
63y5
9 73 3
= 3 7yy2
80d5
8 104 2
2 22 5
= 4 5dd2
150x7
15 10
3 5 5 2
= 5 6xx3
243x13
27 9
9 3
3 3
33
= 9 3xx6