# What is the square root of 45?

Sep 22, 2015

Notice how $45$ has a perfect square factor.

$\sqrt{45}$

$= \sqrt{9} \sqrt{5}$

$= \textcolor{b l u e}{\pm 3 \sqrt{5}}$

Now if you wanted the decimal answer, you could estimate it.

$| \sqrt{4} | = 2$
$| \sqrt{9} | = 3$

You could say with reasonable accuracy that:

$| \sqrt{5} | \approx \frac{5 - 4}{9 - 4} \cdot \left(3 - 2\right) + 2 \approx 2.2$

...making $\sqrt{45} \approx \pm 3 \cdot 2.2 = \pm 6.6$.

In actuality, $| \sqrt{5} | \approx 2.236$, and $\sqrt{45} \approx \pm 6.708$, so it's not too bad of a guess.