Simplify √(7 + 4√3) + 1/√(7 + 4√3)

Published on August 24, 2024

Algebra

Solve for the value of √x + 1/√x given that x = 7 + 4√3. The solution reveals a surprising simplification, resulting in an answer of 4.

Question

Answer

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:

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