SOLUTION: what is the square root of 112?

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Question 897957: what is the square root of 112?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
sqrt%28112%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 112

Factors:

1, 2, 4, 7, 8, 14, 16, 28, 56, 112



Notice how 16 is the largest perfect square, so lets factor 112 into 16*7





sqrt%2816%2A7%29 Factor 112 into 16*7



sqrt%2816%29%2Asqrt%287%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



4%2Asqrt%287%29 Take the square root of the perfect square 16 to get 4



So the expression sqrt%28112%29 simplifies to 4%2Asqrt%287%29



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Check:

Notice if we evaluate the square root of 112 with a calculator we get


sqrt%28112%29=10.5830052442584


and if we evaluate 4%2Asqrt%287%29 we get


4%2Asqrt%287%29=10.5830052442584


This shows that sqrt%28112%29=4%2Asqrt%287%29. So this verifies our answer