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.