Question 280781
The short way to say your problem: Simplify {{{sqrt(84)}}} and then say what number ends up in front of the square root.<br>
Simplifying square roots involves factoring out perfect square factors, if any, and rationalizing denominators. {{{sqrt(84)}}} has no denominators so do not be concerned with rationalizing. All we have to do is see if 84 has any perfect square factors.<br>
4 is a perfect square and it is a factor of 84 so:
{{{sqrt(84) = sqrt(4*21) = sqrt(4)*sqrt(21) = 2sqrt(21)}}}
Like reducing fractions, you keep simplifying square roots until you can go no further. 21 has no perfect square factors so we cannot simplify any further.<br>
Since {{{sqrt(84)}}} simplifies to {{{2sqrt(21)}}}, the answer to the problem is: 2.