What is the square root of 84?

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Answer 1 · 2018-03-10T18:06:53

#+-2sqrt21#

We can break down #sqrt84# into the following:

#sqrt4*sqrt21#

We are able to do this because of the property #sqrt(ab)=sqrta*sqrtb#

Where we can separate the radical into the product of the square root of its factors. #21# and #4# are factors of #84#.

In #sqrt4*sqrt21#, we can simplify to get:

#+-2sqrt21#

*NOTE: The reason we have a#+-#sign is because the square root of #4# can be positive or negative #2#.

#sqrt21# has no perfect squares as factors, so this is the most we can simplify this expression.