1. Objective - To find the square root of a given number.
An operation that yields a number
which, when multiplied by itself,
produces the given number
Squares
Square Roots

2. Are Squares and Square Roots Inverses?
Start
Square it
Root it
Result
It would seem that a square root is the inverse
operation of a square.
Not Exactly!
Does not work with negative numbers.

3. Every positive number has two roots.
Positive Square Root
Negative Square Root
(Principal Square Root)
The square root is not the inverse of a square
because it gives only the positive root.
Consider the following:
Two solutions
One solution

4. Simplify each root below and identify as a
positive root or a negative root.

5. Some square roots need to be estimated using a
calculator.
Check!
Estimate each root below to the nearest hundredth
using a calculator.

6. Perfect Squares
Rational Roots
Irrational Roots

7. Identify each root as rational or irrational.

8. Estimate each irrational root to the nearest tenth
without using a calculator.

9. Determine what two consecutive integers each
irrational root lies between.

10. Determine what two consecutive integers each
irrational root lies between.

11. Finding the Side of a Square 1) 2)
Distance can’t
be negative