Square Roots

Videos to help Grade 8 students learn how to find the square root of small perfect squares and approximate the location of square roots on the number line.

New York State Common Core Math Grade 8, Module 7, Lesson 2

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Lesson 2 Student Outcomes

• Students know that for most integers n, n is not a perfect square, and they understand the square root symbol, √. Students find the square root of small perfect squares.
• Students approximate the location of square roots on the number line.

Lesson 2 Summary

A positive number whose square is equal to a positive number b is denoted by the symbol $$\sqrt {b}$$. The symbol $$\sqrt {b}$$ automatically denotes a positive number.

Perfect squares have square roots that are equal to integers. However, there are many numbers that are not perfect squares.

Lesson 2 Classwork

“How can we determine an estimate for the length of the diagonal of the unit square?” • Consider a unit square, a square with side lengths equal to 1. How can we determine the length of the diagonal, s, of the unit square?

Exercises 1–4
1. Determine the positive square root of 81, if it exists. Explain.
2. Determine the positive square root of 225, if it exists. Explain.
3. Determine the positive square root of -36, if it exists. Explain.
4. Determine the positive square root of , if it exists. Explain.

Exercises 5–9
Determine the positive square root of the number given. If the number is not a perfect square, determine which integer the square root would be closest to, then use “guess and check” to give an approximate answer to one or two decimal places.

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