You may also like

problem icon

Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

problem icon

Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

problem icon

Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

The Root of the Problem

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the sum of $$\frac{1}{\sqrt{1}+ \sqrt{2}}+ \frac{1}{\sqrt{2}+ \sqrt{3}} + \text{and so on up to}+\frac{1}{ \sqrt {99}+ \sqrt{100}}.$$

What other similar sums lead to an exact whole number answer?

You don't need to have learned about summing series to do this problem!