# How do you find the square root of 361?

##### 1 Answer

#### Answer:

See explanation for a few methods...

#### Explanation:

**Prime Factorisation**

One of the best ways to attempt to find the square root of a whole number is to factor it into primes and identify pairs of identical factors. This is a bit tedious in the case of

Let's try each prime in turn:

So

**Approximation by integers**

Subtract half that percentage from the approximation:

The "half that percentage" bit is a form of Newton Raphson method.

Try

**Hmmm, I know some square roots already**

I know

Try

**Memorise**

Hey! I know that already:

Knowing a few squares is useful for all sorts of mental calculation, so I would recommend memorising them a bit. In fact you can multiply two odd or two even numbers using squares, adding, subtracting and halving as follows:

For example: