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• Begin to memorise these important numbers.

• Time how quickly you can recall the first 10 square numbers without looking at a list of numbers.

• Can you go under 5 seconds?

Key Ideas

■ Any whole number multiplied by itself produces a square number

For example: 52 = 5 × 5 = 25. Therefore, 25 is a square number.

• Square numbers are also known as perfect squares

• The first 12 square numbers are:

• All square numbers have an odd number of factors.

• The symbol for squaring is ()2. The brackets are optional, but can be very useful when simplifying more difficult expressions.

■ The square root of a given number is the ‘non-negative’ number that, when multiplied by itself, produces the given number.

• The symbol for square rooting is √ .

• Finding a square root of a number is the opposite of squaring a number.

For example: 42 = 16; hence, √ 16 = 4

We read this as: ‘4 squared equals 16, therefore, the square root of 16 equals 4. ’

• Squaring and square rooting are ‘opposite’ operations.

For example: (√ 7 )2 = 7 also √(7)2 = 7

• A list of common square roots are:

1 Consider a square of side length 6 cm. What would be the area of this shape? What special type of number is your answer?

2 State the first 15 square numbers in index form and as basic numerals.

3 We can confirm that 9 is a square number by drawing the diagram shown at right.

a Explain using dots, why 6 is not a square number.

b Explain using dots, why 16 is a square number.

4 Find: a 62 b 5 squared c (11)2 d 10 to the power of 2 e 72 f 12 × 12

5 Find: a √ 25