Square Roots and Irrational Numbers

The square of an integer is a perfect square. 3 2 1 The square of an integer is a perfect square. The opposite of squaring a number is taking the square root.

Example For example asks what number multiplied by itself is equal to 81? That number is 9. Is there another solution to that problem?

Example For example asks what number multiplied by itself is equal to 81? That number is 9. Is there another solution to that problem? Yes, -9 is also a solution.

Simplify each square root

Simplify each square root 10

Simplify each square root 10 -4

Squares and roots Here is a list that will be helpful:

Do you see that squares and square roots are inverses (opposites) of each other?

Estimating square roots Once we have memorized these squares and their roots, we can estimate square roots that are not perfect squares For example, what about ?

Estimating square roots We find the two perfect squares that are before and after the square root of 8. . . and Look at them on a number line: 2 3

Estimating square roots We can see that is between 2 and 3 but is closer to 3. We would say that is approximately 3. 2 3

TRY THIS: Estimate to the nearest whole number

TRY THIS: Estimate to the nearest whole number 5

TRY THIS: Estimate to the nearest whole number 5 -9

TRY THIS: Estimate to the nearest whole number 5 -9 7

Rational number- can be written as a fraction Irrational number- cannot be written as a fraction because: it is a non-terminating decimal it is a decimal that does NOT repeat * The square roots of ALL perfect squares are rational. * The square roots of numbers that are NOT perfect squares are irrational.

Try This: Identify each number as rational or irrational

Try This: Identify each number as rational or irrational

Try This: Identify each number as rational or irrational

Try This: Identify each number as rational or irrational

Try This: Identify each number as rational or irrational

Try This: Identify each number as rational or irrational