Roots

Part of MathsPowers and roots

Key points

  • , and powers are shown as small digits called .

  • The opposites of squaring and cubing are and .

  • The square root of a number is not always an . When this is the case use the power (√) button on a calculator and round to 1 decimal place.

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Finding the square root

  • Squaring a number is when a number is multiplied by itself. For example, 4² means 4 x 4

  • The opposite of squaring a number is called finding the . The square root is a number whose square is equal to the given number. One square root of 36 is 6 since 6² = 36. 36 also has a negative square root, since (-6)² = 36.

  • There are two roots when calculating the square root of a number (a positive and a negative solution). The two roots could be written individually or using the ± symbol. For example, the two roots of 16 are +4 and -4 could be written as ±4

  • The symbol for the square root is √. For example, √36 means ‘the square root of 36’. The symbol √ refers to the positive square root, so √36 = 6

  • It can be useful to memorise the first 12 square numbers which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144

Examples

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  1. Circling arrows showing the process of squaring and finding the square root. Three going to squared. Squared going to nine. Nine going to square root. Square root going to three.

    This image shows the link between squaring and finding the square root of a number. 3 squared is 9 (because 3² = 3 x 3 = 9). The opposite of squaring a number is called finding the square root. The square root of 9 is 3

Question

What is the square root of 49?

The square root of forty-nine.

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Finding the cube root

  • a number is when a number is multiplied by itself 3 times. For example 4³ means 4 x 4 x 4

  • The opposite of cubing a number is finding the . The symbol for the cube root is ³√

  • The cube root of a number is not always an integer. When this is the case use the ³√ button on a calculator and round to 1 decimal place.

  • It can be useful to memorise the first few cube numbers which are 1, 8, 27, 64, 125 and 216

Examples

Skip image gallery
  1. Circling arrows showing the process of cubing and finding the cube root. Four going to cubed. Cubed going to sixty-four. Sixty-four going to cube root. Cube root going to four.

    This image shows the link between cubing and finding the cube root of a number. 4 cubed is 64 (because 4³ = 4 x 4 x 4 = 64). The opposite of cubing a number is called finding the cube root. The cube root of 64 is 4

Question

What is the cube root of 8?

The cube root of eight.

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Practise roots

Try this quiz to practise roots.

Quiz

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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.

Play the Divided Islands game!
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More on Powers and roots

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