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

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Question 725069: How do I simplify the square root of 4050 step by step
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284050%29
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:
sqrt%2825%2A162%29
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%2825%2A9%2A18%29
9 is a factor of 18, too:
sqrt%2825%2A9%2A9%2A2%29
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, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to split up this square root so that each factor is in its own square root:
sqrt%2825%29%2Asqrt%289%29%2Asqrt%289%29%2Asqrt%282%29
We know what the square roots of the perfect squares are:
5%2A3%2A3%2Asqrt%282%29
Multiplying the numbers that are now outside the square root we get:
45sqrt%282%29
This is the simplified expression.

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