Page 9 - 新思维数学学生用书9 样章

1 Number and calculation

1, 4, 9 and 16 are the first four square numbers. They have integer square roots.

=
2
1 = 1 and 11 2 = 4 and 4 = 2
2
3 = 9 and 9 = 3 4 = 16 and 16 = 4
2
2

What about 2? Is there a rational number n for which n = 2? Remember that you can write a
2
rational number as a fraction.
( ) 2 = 1 × 1 = 2 so 2 must be a little less than 1 .
1
1
1
1
1
1
2
4
2
2
2
( )
5
A closer answer is 1 because 1 5 2 = 2 1 .
12 12 144
( )
An even closer answer is 1 169 because 1 169 2 = 2 1 .
408 408 166464
Do you think you can find a fraction which gives an answer of exactly 2 when you square it?
A calculator gives the answer 2 = 1 414213562. This is a rational number because you can
.
write it as a fraction: 1 414213562 .
1000000000
Is 1.414213562 × 1.414213562 exactly 2?
In this unit, you will look at numbers such as 2.

1.1 Irrational numbers

In this section you will … Key words

• learn about the difference between rational numbers irrational number
and irrational numbers rational number
• use your knowledge of square numbers to estimate surd

square roots
• use your knowledge of cube numbers to estimate
cube roots.

8