SOLUTION: what is the square root of 112?

Question 897957: what is the square root of 112?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Simplifying Square Roots (whole numbers only)

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

Factor 112 into 16*7

Break up the square roots using the identity

Take the square root of the perfect square 16 to get 4

So the expression simplifies to

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Check:

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

and if we evaluate we get

This shows that . So this verifies our answer

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