Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

We'll simplify each root by using the rule: √(ab) = (√a)(√b)

√180 = √(36 x 5) = (√36)(√5) = 6√5 √45 = √(9 x 5) = (√9)(√5) = 3√5 √135 = √(9 x 15) = (√9)(√15) = 3√15

So, \(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\) = (6√5 + 3√5)/(3√15)

= (9√5)/(3√15) = 3/(√3)

Check the answer choices....not there! We must rationalize the denominator. Take 3/(√3) and multiply numerator and denominator by √3 to get: (3√3)/3, which simplifies to √3

Taking \(\sqrt{45}\) common from numerator and denominator \(\sqrt{45}\)(\(\sqrt{4}\)+1) / \(\sqrt{45}\)*(\(\sqrt{3}\)) (2+1)/\(\sqrt{3}\) 3/\(\sqrt{3}\) \(\sqrt{3}\)
_________________

Kudos are always welcome ... as well your suggestions