Page 16 - 新思维数学活动用书7 样章

1.6 Square roots and cube roots

9 Here are some numbers where all the digits are 9:
9 99 999 9999 99999 ...
In numbers where all the digits are 9, which are multiples of 11?

Challenge

10 A number is divisible by 15 if it is divisible by 3 and 5.
a Show that 7905 is divisible by 15.
b The number 208** is divisible by 15. Find the possible values of the two missing digits.

11 Find three numbers less than 20 that are factors of 3729. Give reasons for your answers.
12 Show that 8897 is divisible by only one number between 1 and 12.
13 The numbers 4, 5, 6, … are consecutive numbers; for example, 4567 is a number with four
consecutive digits.
Find all the numbers with four consecutive digits that are divisible by:

a 2 b 3 c 5 d 11

1.6 Square roots and cube roots

Worked example 1.6 Key words

Work out 125 − 49. consecutive
3
cube number
Answer
cube root
5
3
5 = 5 × 5 × 5 = 125, so 125 =.
3
square number
7 = 7 × 7 = 49, so 49 =.
7
2
square root
−
3 125 − 49 = 57 = − 2
Exercise 1.6

Focus

1 Work out:
a 3 + 4 2 b 6² + 7 2 c 9 + 10 2
2
2

15