SOLUTION: Enter the simplified form of square root of 75

Question 119144: Enter the simplified form of square root of 75
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 75

Factors:
1, 3, 5, 15, 25, 75

Notice how 25 is the largest perfect square, so lets factor 75 into 25*3

Factor 75 into 25*3

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

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Check:
Notice if we evaluate the square root of 75 with a calculator we get

and if we evaluate we get

This shows that . So this verifies our answer
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