Grade 8 Radicals: Square Roots

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A square has an area of 144 square inches. How long is each side (in inches)?

   1. A square's area is side × side, so the side is the number that times itself makes 144: √144.
   2. 12 × 12 = 144, so √144 = 12.
   3. So each side is 12 inches.

   Answer: 12

2. Example 2

   √139 is between two consecutive whole numbers. What is the larger one?

   1. Find the perfect squares on each side of 139: 11² = 121 and 12² = 144.
   2. 121 < 139 < 144, so 11 < √139 < 12.
   3. The larger one is 12.

   Answer: 12

3. Example 3

   What is √(1/16)? Write your answer as a fraction.

   1. The square root of a fraction is the square root of the top over the square root of the bottom.
   2. √1 = 1 (1 × 1 = 1) and √16 = 4 (4 × 4 = 16).
   3. So √(1/16) = 1/4.

   Answer: 1/4