SOLUTION: what is the simplify radical of 686

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Question 570944: what is the simplify radical of 686
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28686%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 686


Factors:
1, 2, 7, 14, 49, 98, 343, 686


Notice how 49 is the largest perfect square, so lets factor 686 into 49*14


sqrt%2849%2A14%29 Factor 686 into 49*14

sqrt%2849%29%2Asqrt%2814%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

7%2Asqrt%2814%29 Take the square root of the perfect square 49 to get 7

So the expression sqrt%28686%29 simplifies to 7%2Asqrt%2814%29

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Check:
Notice if we evaluate the square root of 686 with a calculator we get

sqrt%28686%29=26.1916017074176

and if we evaluate 7%2Asqrt%2814%29 we get

7%2Asqrt%2814%29=26.1916017074176

This shows that sqrt%28686%29=7%2Asqrt%2814%29. So this verifies our answer