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Illustrative Math
Grade 8
Let’s approximate square roots.
Illustrative Math Unit 8.8, Lesson 5 (printable worksheets)
In general, we can approximate the values of square roots by observing the whole numbers around it, and remembering the relationship between square roots and squares. Here are some examples:
If we want to find a square root between two whole numbers, we can work in the other direction. For example, since 22^{2} = 484 and 23^{2} = 529, then we know that √500 (to pick one possibility) is between 22 and 23.
Many calculators have a square root command, which makes it simple to find an approximate value of a square root.
Decide if each statement is true or false.
What two whole numbers does each square root lie between? Be prepared to explain your reasoning.
Can we do any better than “between 3 and 4” for √12? Explain a way to figure out if the value is closer to 3.1 or closer to 3.9.
3.5^{2} = 12.25
So, √12 is closer to 3.1 than 3.9
The numbers x, y, and z are positive, and x^{2} = 3, y^{2} = 16, and z^{2} = 30.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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