How do you simplify (2sqrt(7)+35)/[sqrt(7)]?

1 Answer
Zack M.
Nov 4, 2015

2+5sqrt7

Explanation:

It would help if there was something that we could cancel out. At first glance, there is a sqrt7 in the numerator and the denominator, so lets see if we can do something about that. If we factor 35 we get;

35=5*7

But the 7 can be further factored by taking the square root.

7=sqrt7^2=sqrt7*sqrt7

So 35 becomes;

35=5*sqrt7*sqrt7

Now we can start simplifying the expression.

(2sqrt7 + 35)/sqrt7=(2sqrt7 + 5*sqrt7*sqrt7)/sqrt7

Move the sqrt7 out of the numerator.

(sqrt7(2+5sqrt7))/sqrt7

Now the sqrt7s cancel and we have;

(cancelsqrt7(2+5sqrt7))/cancelsqrt7=2+5sqrt7

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