2G Squares and square roots

Learning intentions for this section:

• To understand what it means to square a number or to take its square root

• To know what a perfect square is

• To be able to find the square of a number and the square root of a perfect square Past, present and future learning:

• The concepts in this section may be new to students

• This section prepares students for future work in Stage 4 and beyond

A square number can be illustrated by considering the area of a square with a whole number as its side length.

For example:

Area of square = 4cm × 4cm = 16cm2

Therefore, 16 is a square number.

Another way of representing square numbers is through a square array of dots.

For example:

Numberofdots = 3rowsof3dots = 3 × 3dots = 32 dots = 9dots

Therefore, 9 is a square number.

To produce a square number you multiply the number by itself. All square numbers written in index form will have a power of 2

Finding a square root of a number is the opposite of squaring a number. For example: 42 = 16 and therefore √ 16 = 4.

To find square roots we use our knowledge of square numbers. A calculator is also frequently used to find square roots. Geometrically, the square root of a number is the side length of a square whose area is that number.

Lesson starter: Speed squaring tests

In pairs, test one another’s knowledge of square numbers.

• Ask 10 quick questions, such as ‘3 squared’, ‘5 squared’ etc.

• Have two turns each. Time how long it takes each of you to answer the 10 questions.

• Aim to be quicker on your second attempt.

Write down the first 10 square numbers.