How to simplify $\frac{18}{\sqrt{162}}$
How to simplify $\frac{18}{\sqrt{162}}$?
I tried and got $\frac{2}{\sqrt{2}}$ which is wrong?
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$\begingroup$The systematic way is to do it by factorising numerator and denominator, canceling and finally rationalising the denominator. I'm sure you know this approach, probably having used it (although you didn't follow through in the last step of rationalising the denominator).
The slightly quicker way here is to immediately observe that $18^2 = 324 = 2(162)$, so $\frac{18}{\sqrt {162}} = \frac{\sqrt{324}}{\sqrt {162}} = \sqrt{\frac{324}{162}} =\sqrt 2$.
Try to develop an intuition about numbers that allows you to "see" things like that quickly, it makes math more enjoyable.
Anyway, the likely reason your answer was marked incorrect was because you didn't reasonably simplify as much as you could have. Leaving an irrational expression in the denominator is not generally considered sufficiently simplified. Starting from your "final" answer, multiply both top and bottom by $\sqrt 2$ and see what happens.
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