Page 20 - 新思维数学学生用书8 样章

1.3 Square roots and cube roots

Continued

Answer
a 64 has two square roots. One is 64 = 8 and the other is − 64 = −8
So the equation has two solutions: x = 8 or x = −8

b 3 64 = 4. This means 4 = 4 × 4 × 4 = 64 and so x = 4
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c If x + 64 = 0 then x = −64. So x =−64 =−4
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Exercise 1.3

1 Work out
a 7 2 b (−7) 2 c 7 3 d (−7) 3

2 Find
a 3 125 b 3 −27 c 3 −1 d 3 −8
3 Solve these equations.

a x = 100 b x = 144 c x = 1
2
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d x = 0 e x + 9 = 0
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4 Solve these equations.
a x = 216 b x + 27 = 0
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c x + 1 = 0 d x + 125 = 0
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5 27 = 9 = 729
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Use this fact to find
a 729 b −729 c 3 729 d 3 −729
6 a A calculator shows that 8 − ( − 8) 2 = 0
2
Explain why this is correct.
b Find the value of 4 − ( − 4) . Show your working.
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7 The square of an integer is 100.
What can you say about the cube of the integer?
8 The integer 1521 = 3 × 13 2
2
Use this fact to
a find 1521
b solve the equation x = 1521
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9 a How is −5 different from (−5) ?
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b What is the difference between −5 and (−5) ?
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