How do you simplify #sqrt67/sqrt7#?

2 Answers
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#

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#