Simplify √(7 + 4√3) + 1/√(7 + 4√3)

Published on August 24, 2024

Question

Given that

, we want to find the value of

Step 1: Simplify

Notice that we can rewrite

as follows:

This looks like the expansion of a squared term:

. So, we can write:

Therefore:

Step 2: Find

To find

, we’ll rationalize the denominator:

This simplifies to:

Step 3: Calculate

Finally, substitute the values we found: