SOLUTION: what is the square root of 75 plus the square root of 3

Question 423583: what is the square root of 75 plus the square root of 3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

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.

However, the radicand of one of your square roots has a perfect square factor (other than 1) so it will simplify:

Using a property of radicals, , to split the square root of the product into the product of the square roots of the factors:

The square root of the perfect square simplifies:

Now that we have simplified the square roots, take another look. The terms are now like terms! So we can add them now. Exactly like 5x + x = 6x:

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