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Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
So let's list the factors of 30875
Factors:
1, 5, 13, 19, 25, 65, 95, 125, 247, 325, 475, 1235, 1625, 2375, 6175, 30875
Notice how 25 is the largest perfect square, so lets factor 30875 into 25*1235
Factor 30875 into 25*1235
Break up the square roots using the identity
Take the square root of the perfect square 25 to get 5
So the expression
simplifies to
----------------------------
Check:
Notice if we evaluate the square root of 30875 with a calculator we get
and if we evaluate
we get
This shows that
. So this verifies our answer
