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Roots and powers for AQA A-level Maths

This page covers the following topics:

1. Simplifying roots

The laws of surds can be used to simplify expressions involving surds. Surds can be simplified by finding the factors of the number under the root which are square numbers and evaluating the roots of those numbers.

When the denominator of a fraction involves a surd, the fraction can be simplified by multiplying both the numerator and denominator by that surd. This process is called rationalising the denominator.

Simplifying roots

1

Simplify the following expression: โˆš12 รท โˆš4 ร— โˆš2.

โˆš12 รท โˆš4 ร— โˆš2 = โˆš(12 รท 4) ร— โˆš2 = โˆš3 ร— โˆš2 = โˆš(3 ร— 2) = โˆš6

โˆš6

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2

Maya has drawn a square that has a length of a side of โˆš98. Provide โˆš98 in the form of aโˆšb to find the values of a and b.

โˆš98 = โˆš(49 ร— 2) = โˆš49 ร— โˆš2 = 7โˆš2
Therefore, a = 7 and b = 2.

a = 7, b = 2

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3

Give 3โˆš11 ร— 2โˆš2 in its simplest form.

3โˆš11 ร— 2โˆš2 = 6 ร— โˆš(11 ร— 2) = 6โˆš22

6โˆš22

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