How do you simplify a square root?

Answer 1

Well, first you can see if the square root can be simplified to a whole number, like sqrt36 can be reduced to 6. But if it isn't easily reduced, then you can split the number up into two different factors of that number. Lets take sqrt50. sqrt50 is the same as sqrt(2x25). You know that the sqrt of 25 is 5, so you simply take that out of the root sign, and are left with 5sqrt2.

Answer 2

This usually means:a) Taking any perfect square out of the square root sign. For example, root(12) = root(4) x root(3) = 2 root(3).

b) Rationalizing the denominators. For example, if you have square root of 2 in the denominator, multiply both numerator and denominator by the square root of 2.

Answer 3

If the number under the radical sign has a factor which is a square number greater than 1, then the square root of that number can be taken outside the radical.

For example,

sqrt(75) = sqrt(25*3) = sqrt(25)*sqrt(3) = 5*sqrt(3).