11.2A Simplify and Multiply Square Roots. Squaring a Number When a number is squared, it is multiplied to itself: 1 5525 -3 9 Notice squaring any number.

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Presentation transcript:

11.2A Simplify and Multiply Square Roots

Squaring a Number When a number is squared, it is multiplied to itself: Notice 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 ____________ ______________. squarerooting

Ex 1: Find the square roots of the following numbers: 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.) –5 –23

–m –x

x2x2 2 y3y3

Factor tree inside radical Circle any pairs Multiply pairs w/ # in front Multiply loners back inside

Ex 4: Simplify a) =2 5

b) = 6 2

Ex 4: Simplify c) x x =5 2 x

Ex 4: Simplify d) x x x x x x =2 6 x3x3

Ex 4: Simplify e) x x = 6 2 x

Ex 4: Simplify f) =10 3 y8y8

= g) 70 x5x5

h) = 6 10 y4y4

Multiply #s in front Multiply #s inside Factor tree and simplify

2 35

=35

20x = 2 5 x

240y = 4 15 y5y5

6 5t 6 = 6 5 t3t3

14 12k = 28 3 k4k4

Divide exponent by 2 Leave remainder 1 inside

x x x = x x

= 4 p p2p2

= 2 6k k9k9

= 20 2w w7w7

6 6 = 6 p p3p3

= 2 7x x7x7

63y = 3 7y y2y2

80d = 4 5d d2d2

150x = 5 6x x3x3

243x = 9 3x x6x6