Page 26 - 新思维数学学生用书7 样章

1.6 Square roots and cube roots

1 × 1 × 1 = 1 2 × 2 × 2 = 8 3 × 3 × 3 = 27 Tip

The cube numbers are 1, 8, 27, …
You use an index of 3 and write 1 = 1, 2 = 8, 3 = 27, … The symbol for
3
3
3
You read 1 as ‘1 cubed’ and you read 2 as ‘2 cubed’. cube root is 3 .
3
3
You say ‘2 is the cube root of 8’, which is written as 2 = 8.
3
Worked example 1.11
Work out 64 ÷ 3 64.

Answer

2
8
8 = 64 and so 64 =.
3
3
4 = 64 and so 64 = 4.
Hence, 64 ÷ 3 64 = 8÷ 4 = 2.

You can estimate the square roots of integers that are not square numbers.

Worked example 1.12

a Show that 9 is the closest integer to 79.
b Show that 215 is between 14 and 15.

Answer

2
2
a 9 = 91 and 8 = 64.
79 is between 64 and 81 so 79 is between 8 and 9.
79 is much closer to 81 than to 64 so 9 is the closest integer to 79.
2
b 14 = 196 and 15 = 225.
2
210 is between 196 and 225 and so 215 is between 14 and 15.

Exercise 1.6

1 Copy and complete the following.
a 3 = b 5 = c 8 =
2
2
2
d 10 = e 15 =
2
2
2 An equivalent statement to 7 = 49 is 49 =. Write equivalent statements to your answers to
7
2
Question 1.
3 Find:
a 36 b 81 c 121 d 144

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