Indices are sometimes called powers or exponents.

For example, if y = 4^{2}

then 4 is the base and the power, or index, is 2.

Indices obey laws :-

Rule 1

Example

Rule 2

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Rule 3

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Rule 4

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Rule 5

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A surd is an expression involving unresolved roots of numbers.

To simplify surds, split the number into factors involving square numbers.

Examples

Rule 1

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Rule 2

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Rule 3

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Rule 4

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Rule 5

This is called rationalizing surds ,

the bottom number does not have any square roots.

Examples

Rule 6

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Surds are useful when finding exact values.

Examples

Calculate the exact value of the side marked x in the following triangle :-

Is the following triangle a right-angled triangle ?

Justify your answer.

Calculate the exact value of the area of the following triangle.

Give your answer in its simplest form.

This requires the base , x cm , to be found.