11-1 & 11-2 Squares
and Square Roots
(pgs 470-477)
Indicator: N9  Solve problems
using exponents and square roots
To Square a number: multiply the
number by itself.
Perfect Squares: Squares whose side
lengths (square roots) are rational
numbers. (ex: 1, 4, 9, 16, 25….)
Radical Sign: √
Symbol used to
indicate the square root of a number.
Remember: Squaring and square rooting
are inverse operations so they are located
on the same calculator key (You just need
to push the 2nd key to get to the square
root) Press in the #, 2nd, then x².
4•4 and (-4)•(-4) both equal 16, so 16 has
two square roots √16 is asking for the
positive or principal root = 4.
-√16 is asking for the negative root = -4
+√16 is asking for both = 4 & -4
Find the square of 5
5•5 =25
What is 19 squared
192 = 361
Find √36
√36 = 6
Find √ 676
√ 676= 26
Using squares and square roots
The formula for kinetic energy = ½mv2
If a 6kg ball is soaring through the air at
5m/s, what is its kinetic energy?
= ½ • mv2
= ½ • 6kg• (5m/s)2
= ½ • 6kg•25m2/s2
=75kg•m2/s2
To Estimate… (without a calculator)
First- remember that the square root of a
perfect square is a rational number.
To find an estimate for the square root of a
number that is not a perfect square…

Let’s recall some of the perfect squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100…
Continue estimating
For example: Estimate √96 to the nearest
whole number
Think of your perfect squares…
1, 4, 9, 16, 25, 36, 49, 64, 81, 100…
96 falls between 81 and 100
Which is it closer to?
So, the best estimate for √96 is 10.
To estimate… (with a calculator)
Remember: Press in the #, 2nd, then x²
You can be a little more precise here…
For example: Use a calculator to find the
value of √37 to the nearest tenth.
= 6.08276253… Rounds to ≈ 6.1
Assignment
11-1/ 472 – 473/ 12-28e,29-51
11-2/ 477/ 17-24, 29-32, 35-44