Question 423583
{{{sqrt(75)+sqrt(3)}}}
Like radical terms are the same type of root with the same radicands. (The expression inside a radical is called a radicand.). Your terms are both square roots but their radicands, 75 and 3, are different. So we cannot add them.<br>
However, the radicand of one of your square roots has a perfect square factor (other than 1) so it will simplify:
{{{sqrt(25*3)+sqrt(3)}}}
Using a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, to split the square root of the product into the product of the square roots of the factors:
{{{sqrt(25)*sqrt(3)+sqrt(3)}}}
The square root of the perfect square simplifies:
{{{5*sqrt(3)+sqrt(3)}}}
Now that we have simplified the square roots, take another look. The terms are now like terms! So we can add them now. <i>Exactly</i> like 5x + x = 6x:
{{{5*sqrt(3)+sqrt(3) = 6sqrt(3)}}}