Page 19 - 新思维数学学生用书8 样章

1 Integers

1.3 Square roots and cube roots

In this section you will … Key words

• find the squares of positive and negative integers and cube root
their corresponding square roots natural numbers
• find the cubes of positive and negative integers and rational numbers

their corresponding cube roots
• learn to recognise natural numbers, integers and square root
rational numbers.

5 = 25 Tip
2
This means that the square root of 25 is 5. This can be written as 25 = 5
This is the only answer in the set of natural numbers. The natural
However (−5) = −5 × −5 = 25 numbers are
2
This means that the integer −5 is also a square root of 25. the counting
Every positive integer has two square roots, one positive and numbers and
one negative. zero.
5 is the positive square root of 25 and −5 is the negative square root.
No negative number has a square root.

For example, the integer −25 has no square root because the equation
x = −25 has no solution.
2
5 = 125
3
This means that the cube root of 125 is 5. This can be written as 125 = 5
3
You might think −5 is also a cube root of 125.
However (−5) = −5 × −5 × −5 = (−5 × −5) × −5 = 25 × −5 = −125
3
3
So −125 = −5
Every number, positive or negative or zero, has only one cube root.

Worked example 1.3

Solve each equation.
a x = 64
2
b x = 64
3
c x + 64 = 0
3

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