Square Roots and Irrational Numbers 1 2 3

Square Roots and Irrational Numbers

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

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

Example n 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 n Here is a list that will be helpful:

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

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

Estimating square roots n n n 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 n 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

n Rational fraction number- can be written as a n 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 Irrational

Try This: Identify each number as rational or irrational Irrational Rational

Try This: Identify each number as rational or irrational Irrational Rational

Try This: Identify each number as rational or irrational Irrational Rational

Try This: Identify each number as rational or irrational Irrational Rational Irrational