Question 135422: Tutor: How do Isubtract and simplify 5 square root of 20 minus 2 square root of 125? Found 2 solutions by nycsharkman, Earlsdon:Answer by nycsharkman(136) (Show Source):
You can put this solution on YOUR website! How do I subtract and simplify 5 square root of 20 minus 2 square root of 125?
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.
You can put this solution on YOUR website! Simplify:
The key here is to factor the radicand (the quantity under the radical), then, if any of these factors are perfect squares, take their square root and move the result outside of the radical. Rewrite this as: Take the square roots of the squares and move them outside. = 0
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