# What is square root 73 in its simplest form?

Dec 29, 2017

$= \sqrt{73}$

#### Explanation:

This question will require the idea of prime factorisations

Every natual number can be written as a product of prime numbers

Example:

 24 = color(blue)(2 * 12) = color(green)(2 * 3 * 4) = color(purple)(2 * 3 * 2 * 2 = color(red)(2^3 * 3

$\implies 24 = {2}^{3} \cdot 3$ This is the prime factorisation...

So $\sqrt{24} = \sqrt{{2}^{3} \cdot 3} = \sqrt{{2}^{2} \cdot 2 \cdot 3} = \sqrt{{2}^{2}} \cdot \sqrt{2} \cdot \sqrt{3}$

$\implies \sqrt{24} = 2 \cdot \sqrt{2} \cdot \sqrt{3} = 2 \sqrt{6}$

Using our knowledge of: $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

We know $73 = 73 \cdot 1$ - its prime!

$\sqrt{73} = \sqrt{1} \cdot \sqrt{73} = \sqrt{73}$

This can not be reduced any more, $\sqrt{73}$ is in simplest form

$\sqrt{p}$ in its simpelst form if $p$ is a prime number