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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
Factor 686 into 49*14
Break up the square roots using the identity
Take the square root of the perfect square 49 to get 7
So the expression
simplifies to
----------------------------
Check:
Notice if we evaluate the square root of 686 with a calculator we get
and if we evaluate
we get
This shows that
. So this verifies our answer
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