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

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Question 423583: what is the square root of 75 plus the square root of 3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2875%29%2Bsqrt%283%29
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:
sqrt%2825%2A3%29%2Bsqrt%283%29
Using a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to split the square root of the product into the product of the square roots of the factors:
sqrt%2825%29%2Asqrt%283%29%2Bsqrt%283%29
The square root of the perfect square simplifies:
5%2Asqrt%283%29%2Bsqrt%283%29
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:
5%2Asqrt%283%29%2Bsqrt%283%29+=+6sqrt%283%29