# How do you multiply sqrt[5] * sqrt[5]?

Jun 21, 2016

5

#### Explanation:

Writing this another way we have ${\left(\sqrt{5}\right)}^{2}$

${\left(\sqrt{5}\right)}^{2} = 5$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b r o w n}{\text{How squaring a square root works}}$

$\textcolor{b l u e}{\text{Point 1}}$
Squaring the square root has almost the same effect of not having taken the square root in the first place.

$\textcolor{b l u e}{\text{Point 2}}$
Suppose we write the square root of 5 as $x$.

Then $\left(- x\right) \times \left(- x\right) = + 5$
and $\left(+ x\right) \times \left(+ x\right) = + 5$

So $\sqrt{5}$ has 2 answers. These are a positive value and also a the same number but it is negative. ( $+ x \text{ or } - x$ ).

$\textcolor{b l u e}{\text{Point 3}}$
As the whole thing is squared then it does not matter if we look at $- x$ or $+ x$ as the answer is always going to be +5

as $\left(- x\right) \times \left(- x\right) = + 5 \text{ and } \left(+ x\right) \times \left(+ x\right) = + 5$