How to Simplify a Complex Surd to Its Simplest Form

Hello amazing people! Welcome to another beautiful day. Still on the topic of Surds, I’ll be simplifying a complex surd expression to its simplest form.

I began by breaking down the complex surds into factors that contain perfect squares. After that, I found the square roots of those perfect squares to obtain single numerical values, which I then multiplied by the remaining surds that were split earlier.

Next, I factored out the common terms from the entire expression — in this case, the square root of 2 (√2) and then cancelled out the similar factors in both the numerator and denominator. After simplifying completely, the final answer was 8.

That’s the full process of simplifying a complex surd expression, and I hope you find this explanation educative and helpful.

See below the step-by-step workings;