Roots

Take a deep breath, and get ready to tackle this page.

“Squared” means “multiplied by itself”: 8² = 8 × 8 = 64

Square root is the reserve process: square root of 64 = 8

“Square Root” means “what number times by itself gives…”

EXAMPLES
1. What is square root of 49?

7 times by itself gives 49: 49 = 7 × 7 so square root of 49 = 7

2. What is square root of 29.16? Use your calculator. Press: square root of 29.16 = 5.

3. Find both square roots of 36. 6 × 6 = 36, so positive square root = 6 -6 x -6 = 36, so negative square root = -6

All numbers also have a negative square root - it’s just the “-” version of the normal positive one.

This little rule for multiplying roots might come in handy in your exam: square root of a x square root of a = a

Be careful - this is only true if you’re multiplying together two roots which are the same.

“Cubed” means “multiplied by itself and then by itself again”: 2³ = 2 × 2 × 2 = 8

Cube root is the reverse process: cube root of 8 = 2

“Cube root” means “what number times by itself and then by itself again gives…”

You need to be able to write down the cube roots of the cube numbers given on p.1 without a calculator.

To find the cube root of any other number you can use your calculator - press cube root.

EXAMPLES
1. What is the cube root of 27? 3 times by itself and then by itself again gives 27: 27 = 3 × 3 × 3 So cube root of 27 = 3 27 is a cube number.

2. What is the cube root of 4913? Press: cube root of 4913 = 17

You can use your calculator to find any root of a number, using the cube root x or buttons.

Make sure you know how to use your calculator to find higher order roots - the buttons might be slightly different to these ones.

Learn the difference between square roots and square numbers

A square root is a number that, when multiplied by itself, gives the number under the root symbol.

Q1) Find a) square root of 196 without using a calculator. 14

b) cube root of 9261 = 21

c) 7 square root of 2187 = 3273

Q2) The volume of a cube is 1.728cm³. Find the length of one of its sides, in cm. 3.21

Q3) Work out the cube root of 19.34 + (1.3 + 2.5)². Write down the full calculator display. 17.1242244213