# Rationalising the denominator problem

I need help rationalising this

$$\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1) }$$

I'm so stuck with this problem!

• Treat it like a product of four fractions. Rationalize the denominator of each factor, and multiply. – D.B. Mar 4 at 3:20

The deepest root is the place to start. Multiply top and bottom by $$\sqrt[16]5-1$$. You don't have any more sixteenth roots, so this is progress. Keep going.
• Once you remove the sixteenth root others will automatically be removed from the formula $(a+b)(a-b) =a^2 - b^2$ – Abhinav Mar 4 at 3:43