DIRECTIONS: Fill every gap in both tables, then work out Part C.
√144 = 12, because 12 × 12 = 144.
3√125 = 5, because 5 × 5 × 5 = 125.
Part A — The perfect squares. Fill every gap.
n
n²
n
n²
n
n²
1
6
36
11
2
4
7
49
12
3
8
13
4
16
9
14
196
5
10
15
225
Part B — The perfect cubes.
n
1
2
3
4
5
n³
64
125
Part C — Evaluate.
3.
√100 =
4.
√64 =
5.
√25 =
6.
3√−64 =
7.
3√8 =
Square Roots and Cube Roots — continued
Grade 8 · Number · Page 2 of 2
x² = 49 has two answers, 7 and −7. But √49
means only the positive one: 7.
Part D — Solve. Give every answer the equation has.
8.
x² = 196 x = or x =
9.
x² = 225 x = or x =
10.
x² = 121 x = or x =
11.
x³ = −27 x =
Part E — Explain it.
Priya solves x² = 81 and writes x = 9. She is not wrong, but she is not finished. What is missing — and why does √81 = 9 have only the one answer?
In Part C you worked out 3√−64, and it is a perfectly ordinary number. But √−64 is not a number at all. What is the difference between cubing and squaring that causes that?