How do you simplify sqrt67/sqrt7?

2 Answers
Faizan B.
Mar 22, 2015

When we simplify this problem, we are rationalizing the denominator.

For info on how to do this, check this site out: http://www.purplemath.com/modules/radicals5.htm

Now, let's solve this problem:

First thing, we multiply the expression by sqrt(7)/sqrt(7). We can do this because sqrt(7)/sqrt(7) is simply 1, and multiplying something by 1 doesn't change the nature of the expression.

So, our expression is this: sqrt(67)/sqrt(7) * sqrt(7)/sqrt(7)

Multiplying, we get: sqrt(469)/sqrt(49)

Since sqrt(49) simplifies to 7, we get: sqrt(469)/7

Since, sqrt(469) is not something we can simplify, our final answer is: sqrt(469)/7

Kevin B.
Mar 22, 2015

In a calculator, the answer is 3.09377254682

If by simply, you mean to rationalize the denominator, multiple both the numerator and the denominator by sqrt(7):

(sqrt(67)/sqrt(7)) = ((sqrt(67) * sqrt(7)) / 7) = sqrt(469)/7

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