1.3.7

Roots

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Roots

Roots are the opposite of powers.

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Square root

  • √25 means the number that squares to give 25.
    • 5 is a square root of 25 because 5 × 5 = 25
    • -5 is a square root of 25 because -5 × -5 = 25
    • We write the answer as √25 = ±5.
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Square root

  • There will always be two square roots of a number - one positive and one negative.
    • Negative numbers have no square roots.
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Cube root

  • 3√8 means the number that cubes to give 8.
    • 2 × 2 × 2 = 8 therefore 3√8 = 2.
    • Since (-2)3 = -8 there is only ever one cube root of a number.
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Nth root

  • n√x means the number that when raised to the power of n gives x.
    • There will be positive and negative roots if n is even, and only a positive root if n is odd.

Jump to other topics

1Number

1.1Place Value

1.2Factors & Multiples

1.3Operations

1.4Fractions, Decimals & Percentages

1.5Growth & Decay

1.6Measurements & Units

1.7Accuracy

2Algebra

3Ratio, Proportion & Rates of Change

4Geometry & Measures

5Probability

6Statistics

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