Page 28 - 新思维数学学生用书7 样章

1.6 Square roots and cube roots

Think like a mathematician

12 1 = 1 and 2 = 4 and so 2 − 1 = 3.
2
2
2
2
1 and 2 are consecutive square numbers. The difference between 1 and 2
2
2
2
2
is 3.
a Copy and complete this diagram, showing the differences between
consecutive square numbers.
Square numbers: 1 2 3 4 5 6 2
2
2
2
2
2
Difference: 3
b Describe any pattern in your answers.
c Investigate the differences between consecutive cube numbers.
Cube numbers: 1 2 3 4 5 6 3
3
3
3
3
3
Difference: 7
13 a Work out:
3
3
3
3
i 1 ii 1 + 2 3 iii 1 + 2 + 3 3
b What do you notice about your answers to part a?
c Does the pattern continue when you add more cube numbers? Give a reason for your
answer.
d Compare your answer to part c with a partner’s. Can you improve your answer?
14 a Add up the first three odd numbers and find the square root of the answer.
b Add up the first four odd numbers and find the square root of the answer.

c Can you generalise the results of parts a and b?
d Look at this diagram.

How is this diagram connected with the earlier parts of this question?

Summary checklist

I can find square numbers and their corresponding square roots.
I can find cube numbers and their corresponding cube roots.

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