Question 725069
{{{sqrt(4050)}}}
Simplifying square roots like this one involves finding as many perfect square factors of the radicand as possible. ("Radicand" is the name for the expression inside a radical.)<br>
So we are looking for perfect square factors in 4050. This is a fairly large number and it has many factors. But if it ends in 50 it must have 25 as a factor:
{{{sqrt(25*162)}}}
If we know the divisibility rule for 9 we will know that 9 is a factor of 162. (If we don't know the rule then we just have to divide by 9 and find out that it divides evenly.)
{{{sqrt(25*9*18)}}}
9 is a factor of 18, too:
{{{sqrt(25*9*9*2)}}}
With no perfect square factors in 2 (other than 1 which doesn't really matter) we are finished finding perfect square factors.<br>
Next we use a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, to split up this square root so that each factor is in its own square root:
{{{sqrt(25)*sqrt(9)*sqrt(9)*sqrt(2)}}}
We know what the square roots of the perfect squares are:
{{{5*3*3*sqrt(2)}}}
Multiplying the numbers that are now outside the square root we get:
{{{45sqrt(2)}}}
This is the simplified expression.<br>
P.S. The 162 came from the fact that 4050/25 = 162