11.2A
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Transcript of 11.2A
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11.2A
Simplify and Multiply Square Roots
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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
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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
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Ex 1: Find the square roots of the following numbers:
9
1
232
m2
25
3 1
23 m
Not possible!
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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
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m2 –m
–x
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x22y3
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Factor tree inside radicalCircle any pairsMultiply pairs w/ # in frontMultiply loners back inside
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Ex 4: Simplify
a) 205 4
2 2
= 2 5
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2 36
6 6
72
23 23
b)= 6 2
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Ex 4: Simplify
c) 250x2 25
5 5
x x
= 5 2x
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Ex 4: Simplify
d) 624x2 12
2 6
2 3
x x x x x x
= 2 6x3
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Ex 4: Simplify
e) 22 18x
2 9
3 3
x x
= 6 2x
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Ex 4: Simplify
f) 165 12y
3 4
2 2
= 10 3y8
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10 10
107 100x =g)
70x5
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h)
5 8
4 2
83 40y
2 2
= 6 10y4
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Multiply #s in frontMultiply #s insideFactor tree and simplify
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2 35
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5 49
7 7
= 35
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20x2
5 4
2 2
= 2 5x
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240y10
24 10
6 4
3 2 2 22 5
= 4 15y5
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6 5t6 = 6 5t3
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14 12k8
4 3
2 2
= 28 3k4
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Divide exponent by 2Leave remainder 1 inside
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x x x
= xx
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= 4 pp2
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6 4
3 2 2 2
= 2 6kk9
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8 4
4 22 2
22
= 20 2ww7
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6 6
= 6 pp3
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7 42 2
= 2 7xx7
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63y5
9 73 3
= 3 7yy2
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80d5
8 104 2
2 22 5
= 4 5dd2
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150x7
15 10
3 5 5 2
= 5 6xx3
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243x13
27 9
9 3
3 3
33
= 9 3xx6