SOLUTION: How do I simplify the square root of 4050 step by step

Question 725069: How do I simplify the square root of 4050 step by step
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

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.)

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:

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.)

9 is a factor of 18, too:

With no perfect square factors in 2 (other than 1 which doesn't really matter) we are finished finding perfect square factors.

Next we use a property of radicals, , to split up this square root so that each factor is in its own square root:

We know what the square roots of the perfect squares are:

Multiplying the numbers that are now outside the square root we get:

This is the simplified expression.

P.S. The 162 came from the fact that 4050/25 = 162
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