What is the square root of 45?

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Answer 1 · 2015-09-22T02:46:50

Notice how $45$ has a perfect square factor.

$sqrt45$

$= sqrt9sqrt5$

$= color(blue)(pm3sqrt5)$

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

$|sqrt4| = 2$
$|sqrt9| = 3$

You could say with reasonable accuracy that:

$|sqrt5| ~~ (5-4)/(9-4)*(3-2)+2 ~~ 2.2$

...making $sqrt45 ~~ pm3*2.2 = pm6.6$ .

In actuality, $|sqrt5| ~~ 2.236$ , and $sqrt45 ~~ pm6.708$ , so it's not too bad of a guess.