Estimating Square Roots and Cube Roots

Review of Perfect Square Roots

What About This?

√−25

Rule

• You cannot take the square root of a negative number because no rational number can be squared to produce a negative product.

What About This Then?

−√25

Non – Perfect Roots

• As you know, most square roots cannot be represented with a single integer. However, we can estimate the roots to be between two integers, and further estimate the root to the tenths place, hundredths place and so on.

Think Pair Share

• Why are you unable to provide an exact answer for all square roots?

• “An exact answer cannot be calculated for all square roots because….”

Estimating Roots Between Integers

Let’s start nice and easy:

Estimate the square rootof 12 between two integers

Estimating Roots Between Integers

Let’s start nice and easy:

Estimate the square rootof 30 between two integers

Estimating Roots Between Integers

Let’s start nice and easy:

Estimate the square rootof 70 between two integers

Estimating Roots Between Integers

Let’s start nice and easy:

Estimate the square rootof 110 between two integers

Estimating to the Tenths Place

• Once we estimate the square root between two integers, we can begin to improve the accuracy of our estimate to the tenths place.

Informally

• Estimate the square root of 20.

Informally

• Estimate the square root of 55.

Informally

• Estimate the square root of 63.

Informally

• Estimate the square root of 40.

Cube Roots

=

Your Turn

3√729

What About This

3√−8

Non Perfect Cube Roots

Estimate the cube root between two integers:

3√50

Non Perfect Cube Roots

Estimate the cube root between two integers:

3√200

Rule

• You can take the cube root of a number because a negative integer cubed always produces a negative product.

Closure

• How do you estimate a square root between two integers?

Closure

• Why can you take the cube root of a negative number, but not the square root of a negative number?