SOLUTION: Enter the simplified form of square root of 300

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Question 119146: Enter the simplified form of square root of 300
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28300%29 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 300
Factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300


Notice how 100 is the largest perfect square, so lets factor 300 into 100*3


sqrt%28100%2A3%29 Factor 300 into 100*3

sqrt%28100%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

10%2Asqrt%283%29 Take the square root of the perfect square 100 to get 10

So the expression sqrt%28300%29 simplifies to 10%2Asqrt%283%29

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Check:
Notice if we evaluate the square root of 300 with a calculator we get

sqrt%28300%29=17.3205080756888

and if we evaluate 10%2Asqrt%283%29 we get

10%2Asqrt%283%29=17.3205080756888

This shows that sqrt%28300%29=10%2Asqrt%283%29. So this verifies our answer