# What is the square root of 204?

Mar 15, 2018

The square root of 204 is 2$\sqrt{51}$

#### Explanation:

You need to try finding a perfect square of 204. So there are many ways you can get to 204 but you are trying to find a perfect square of 204. So 4 x 51 = 204. So in the house, you should have $\sqrt{4 \cdot 51}$. So the only number you can take outside of the house is a 2. Your final answer is 2$\sqrt{51}$

Mar 15, 2018

$\sqrt{204} = 2 \sqrt{51} \leftarrow$ Exact answer.

$\sqrt{204} \approx 14.283$ to 3 decimal places - Approximate answer.

#### Explanation:

This question is posted under 'simplification of radicals.' and that is applied in the solution.

The objective is to find any squared values that can be used to make 204. These can be 'taken outside' the square root. If you can not spot them use a prime factor tree. It does not have to be need. A quick and very rough sketch in the margin will do.

From the above diagram note that the only squared prime number is 2.

${2}^{2} \times 3 \times 17 \textcolor{w h i t e}{\text{ddd")->color(white)("ddd}} {2}^{2} \times 51$

So we have $\sqrt{204} = \sqrt{{2}^{2} \times 51} = 2 \sqrt{51} \leftarrow$ Exact answer.

Using a calculator $\to \sqrt{204} = 14.282856 \ldots \ldots .$

Giving:

$\sqrt{204} \approx 14.283$ to 3 decimal places - Approximate answer.

Where the symbol $\approx$ means 'approximately equal to'