Virginia SOL Math / Grade 7 / Number & Number Sense

7.NS.3

Square Roots & Perfect Squares

What you'll learn

  • Identify perfect squares up to 400
  • Find the positive square root of a perfect square
  • Estimate the square root of a non-perfect square between two whole numbers

Words to know

Perfect square —
a number made by multiplying a whole number by itself
Square root —
a number that multiplies by itself to give the original number
Radical sign —
the symbol used to show a square root
Base —
the number being raised to a power
Estimate —
a close, reasonable value

Why it matters Square roots undo squaring, which helps us find a side length from an area and prepares us for the Pythagorean Theorem in later grades.

Worked examples

Model ItI do

Find the square root of 144.

Ask what number times itself equals 144. Since 12 times 12 = 144, the square root of 144 is 12.

Try It TogetherWe do

Between which two whole numbers does the square root of 50 lie?

Find perfect squares near 50: 49 = 7 squared and 64 = 8 squared. Since 50 is between them, the square root of 50 is between 7 and 8, and closer to 7.

Now YouYou do

Find the square root of 81.

Ask what whole number times itself gives 81. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find 4 squared.

  2. 2.Find the square root of 25.

  3. 3.Is 16 a perfect square?

On Level

The core Quick Check from the book.

  1. 1.Find the square root of 64.

  2. 2.Is 20 a perfect square? Explain briefly.

  3. 3.The square root of 30 lies between which two whole numbers?

  4. 4.Find 9 squared.

  5. 5.Find the square root of 225.

Challenge

Stretch your thinking.

  1. 1.The square root of 90 lies between which two whole numbers?

  2. 2.Find the square root of 196.

  3. 3.A square garden has an area of 169 square feet. Find the length of one side.