kerrum75

2021-12-20

What is the square root of 45?

Medicim6

Beginner2021-12-21Added 33 answers

Notice how 45 has a perfect square factor.

$\sqrt{45}$

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

$=\pm 3\sqrt{5}$

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

$\left|\sqrt{4}\right|=2$

$\left|\sqrt{9}\right|=3$

You could say with reasonable accuracy that:

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

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

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

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

You could say with reasonable accuracy that:

...making

In actuality,

kaluitagf

Beginner2021-12-22Added 38 answers

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:

$6.70820393\dots$

Pull terms out from under the radical.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

RizerMix

Expert2021-12-29Added 656 answers

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