Estimating Square Roots and Cube Roots. Review of Perfect Square Roots.
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Transcript of Estimating Square Roots and Cube Roots. Review of Perfect Square Roots.
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?