# What is the square root of 45?

What is the square root of 45?
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Medicim6
Notice how 45 has a perfect square factor.
$\sqrt{45}$
$=\sqrt{9}\sqrt{5}$
$=±3\sqrt{5}$
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 $\sqrt{45}\approx ±3\cdot 2.2=±6.6$
In actuality, $|\sqrt{5}|\approx 2.236$ , and $|\sqrt{45}|\approx ±6.708$ , so it's not too bad of a guess.
###### Not exactly what you’re looking for?
kaluitagf
Rewrite 45 as ${3}^{2}\cdot 5$
$\sqrt{{3}^{2}\cdot 5}$
Pull terms out from under the radical.
$3\sqrt{5}$
The result can be shown in multiple forms.
Exact Form:
$3\sqrt{5}$
Decimal Form:
$6.70820393\dots$
###### Not exactly what you’re looking for?
RizerMix

$45=9\cdot 5$
$\sqrt{45}=\sqrt{9}\sqrt{5}=3\cdot \sqrt{5}$