What is the square root of 45?

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What is the square root of 45?

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Answer 1 · 2015-09-22T02:46:50

Notice how $45$ $45$ has a perfect square factor.

$\sqrt{45}$ $sqrt45$

$= \sqrt{9} \sqrt{5}$ $= sqrt9sqrt5$

$= \pm 3 \sqrt{5}$ $= color(blue)(pm3sqrt5)$

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

$∣ ∣ \sqrt{4} ∣ ∣ = 2$ $|sqrt4| = 2$
$∣ ∣ \sqrt{9} ∣ ∣ = 3$ $|sqrt9| = 3$

You could say with reasonable accuracy that:

$∣ ∣ \sqrt{5} ∣ ∣ \approx \frac{5 - 4}{9 - 4} \cdot (3 - 2) + 2 \approx 2.2$ $|sqrt5| ~~ (5-4)/(9-4)*(3-2)+2 ~~ 2.2$

...making $\sqrt{45} \approx \pm 3 \cdot 2.2 = \pm 6.6$ $sqrt45 ~~ pm3*2.2 = pm6.6$ .

In actuality, $∣ ∣ \sqrt{5} ∣ ∣ \approx 2.236$ $|sqrt5| ~~ 2.236$ , and $\sqrt{45} \approx \pm 6.708$ $sqrt45 ~~ pm6.708$ , so it's not too bad of a guess.

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What is the square root of 45?

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