Question

Simplify square root of 5 plus the square root of 125 plus 25. I don't understand. Can someone please help me?

Answer 1

5(sqrt{20}) - 2(sqrt{125})
You need to simplify the square roots individually.
For each square root, look for two numbers that, when multiplied, will yield the number inside the radicand. However, one of the factors has to be a perfect square.
sqrt{20} = sqrt{4} times sqrt{5}
The square root of 4 is a perfect square because 2 times 2 = 4.
Then, the square root of 4 = 2.
The square root of 5 is NOT a perfect square and it is also in lowest term.
So, leave it alone.

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sqrt{125} = sqrt{25} times sqrt{5}
The square root of 25 is 5 because 5 times 5 = 25.
Then, the square root of 25 is 5.
Again, the square root of 5 is NOT a perfect square and it is also in lowest term. Leave it alone.
We now have this:
5(2)(sqrt{5}) - 2(5)(sqrt{5})
10(sqrt{5}) - 10(sqrt(5}) = 0
The answer is 0.

Answer 2

√ 5 + √ 125 + 25 [original problem - I assume 25 is not under a root]

√5 + √ 25·5 + 25 [find perfect square factors of 125]
√5 + 5√5 +25 [simplify √125]
6√5 + 25 [add 1√5 + 5√5 together]


***If the 25 is under a root, simply take it's square root (5) and add it to the end of the problem. The answer would be 6√5 + 5***