Grade 8 Radicals: Unit Review

Worked examples

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

1. Example 1

   A square has an area of 529 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 529: √529.
   2. 23 × 23 = 529, so √529 = 23.
   3. So each side is 23 inches.

   Answer: 23

2. Example 2

   A right triangle has a hypotenuse of 37 in and one leg of 35 in. How long is the other leg (in inches)?

   1. In a right triangle, a² + b² = c², where c is the hypotenuse — the longest side, across from the right angle.
   2. b² = 37² − 35² = 1369 − 1225 = 144.
   3. b = √144 = 12, because 12 × 12 = 144.
   4. So the other leg is 12 inches.

   Answer: 12

3. Example 3

   What is ∛(−64)?

   1. ∛(−64) is the number that, used 3 times as a factor, makes −64.
   2. 4 × 4 × 4 = 64, and three negatives multiply to a negative: (−4) × (−4) × (−4) = −64.
   3. So ∛(−64) = −4.

   Answer: −4