Page 10 - 新思维数学活动用书8 样章

1.3 Square roots and cube roots

1.3 Square roots and cube roots

Exercise 1.3 Key words

natural numbers
Focus rational numbers
1 Work out
a 14 2 b (−14) 2 c (−20) 2 d (−30) 2

2 Work out
a 4 3 b (−6) 3 c (−10) 3 d (−1) + (−1) 3
2
3 If possible, work out
a −64 b 3 −64 c 3 −125 d 3 −729

Practice

4 Solve each equation.

2
2
2
2
a x = 25 b x = 225 c x − 81 = 0 d x + 121 = 0
5 Solve each equation.
3
3
3
3
a x = 216 b x = −216 c x + 1000 = 0 d x + 8000 = 0
2
3
6 23 = 529 and 23 = 12 167
Use these facts to solve the following equations.
a x = 529 b x + 529 = 0 c x = 12 167 d x + 12 167 = 0
2
3
3
2
7 Write whether each statement is true or false.
a 9 is a rational number
b −9 is a natural number
c 99 is an integer
d −999 is both an integer and a rational number
e 9999 is both a natural number and a rational number

Challenge

8 a Copy and complete this table.

x −3 −2 −1 0 1 2

x + x 0
2
x + x 0
3
b Use the table to solve these equations.
i x + x = 2 ii x + x = 2
3
2

9