# Indices

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## Indices

Another name for **index** is **power** (you will often say, for example, 2 to the power of three to mean 2^{3}).

**In order to work with indices you need to learn the basic laws of indices listed below:**

We know that √9 and √36 have exact values of 3 and 6 respectively.

However √2 and √3 does not have an exact quantity and these numbers are called **irrational**.

Surds are just the name given to the numbers when they are left in the form √2 and √3.

**There is only one rule you need to remember:**

√(ab) = √a √b

**This allows us to express a number in simplest surd form:**

**For example:**

√50 = √(2 × 25) = √2 × √25 = √2 × 5 = 5 √2

If you have a fractional answer, you must remove the surds from the denominator - this is called **rationalizing the denominator**.

Read the following example to see how this is done.

**Example:**

**Simplify **

From our work on expanding brackets we know that (a + b)(a − b) gives a^{2} − b^{2} and we eliminate any surds contained in a or b.

So to rationalize the denominator of

we must multiply the numerator and the denominator by √6 + √5.

**Multiplying the denominators gives:**