11-1 & 11-2 Squares 11-1 & 11-2 Squares and Square Rootsand Square Roots

(pgs 470-477)(pgs 470-477)

Indicator: N9 Indicator: N9 Solve problems Solve problems using exponents and square rootsusing exponents and square roots

To To SquareSquare a number: multiply the a number: multiply the number by itself.number by itself.

Perfect SquaresPerfect Squares: Squares whose side : Squares whose side lengths (square roots) are rational lengths (square roots) are rational numbers. (ex: 1, 4, 9, 16, 25….)numbers. (ex: 1, 4, 9, 16, 25….)

Radical SignRadical Sign: : √ Symbol used to √ Symbol used to indicate the square root of a number.indicate the square root of a number.

Remember: Squaring and square rooting Remember: Squaring and square rooting are are inverse operations inverse operations so they are located so they are located on the same calculator key (You just need on the same calculator key (You just need to push the to push the 22ndnd key to get to the square key to get to the square root) Press in the #, root) Press in the #, 22ndnd, then x, then x².².

44••4 and (-4)4 and (-4)••(-4) both equal 16, so 16 has (-4) both equal 16, so 16 has two square roots two square roots √16 is asking for the √16 is asking for the positive or positive or principal rootprincipal root = 4. = 4.

-√16 is asking for the negative root = -4-√16 is asking for the negative root = -4

++√16 is asking for both = 4 & -4√16 is asking for both = 4 & -4

Find the square of 5Find the square of 5

55••5 =255 =25

What is 19 squaredWhat is 19 squared

191922 = 361 = 361

Find Find √36√36

√√36 = 636 = 6

Find √ 676Find √ 676

√ √ 676= 26676= 26

Using squares and square rootsUsing squares and square roots

The formula for kinetic energy = ½mvThe formula for kinetic energy = ½mv22

If a 6kg ball is soaring through the air at If a 6kg ball is soaring through the air at 5m/s, what is its kinetic energy? 5m/s, what is its kinetic energy?

= ½ = ½ • • mvmv22

= ½ = ½ • • 6kg6kg•• (5m/s) (5m/s)22

= ½ = ½ • • 6kg6kg••25m25m22/s/s22

=75kg=75kg••mm22/s/s22

To Estimate… To Estimate… (without a calculator)(without a calculator)

First- remember that the square root of a First- remember that the square root of a perfect square is a rational number.perfect square is a rational number.

To find an estimate for the square root of a To find an estimate for the square root of a number that is not a perfect square…number that is not a perfect square…

Let’s recall some of the perfect squares-Let’s recall some of the perfect squares-

1, 4, 9, 16, 25, 36, 49, 64, 81, 100… 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

Continue estimatingContinue estimatingFor example: Estimate For example: Estimate √96 to the nearest √96 to the nearest whole numberwhole number

Think of your perfect squares…Think of your perfect squares…

1, 4, 9, 16, 25, 36, 49, 64, 81, 100…1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

96 falls between 81 and 10096 falls between 81 and 100

Which is it closer to? Which is it closer to?

So, the best estimate for So, the best estimate for √96 is 10.√96 is 10.

To estimate… (with a calculator)To estimate… (with a calculator)

Remember: Press in the #, Remember: Press in the #, 22ndnd, then x, then x²²

You can be a little more precise here…You can be a little more precise here…

For example: Use a calculator to find the For example: Use a calculator to find the value of value of √37 to the nearest tenth.√37 to the nearest tenth.

= 6.08276253… Rounds to = 6.08276253… Rounds to ≈ 6.1

AssignmentAssignment

11-1/ 472 – 473/ 12-28e,29-5111-1/ 472 – 473/ 12-28e,29-51

11-2/ 477/ 17-24, 29-32, 35-44 11-2/ 477/ 17-24, 29-32, 35-44