Discussion

Explanation:

Square root of 14 + 6√5 will be of the form √x + √y.

∴ (√x + √y)² = 14 + 6√5

⇒ x + y + 2√xy = 14 + 6√5

Now, rational part of RHS = rational part on LHS
⇒ x + y = 14   …(1)

Also, irrational part of RHS = irrational part on LHS
⇒ 2√xy = 6√5
⇒ xy = 45   …(2)

Solving (1) and (2), we get
x = 9 and y = 5 or x = 5 and y = 9.

In both cases square root of 14 + 6√5 = 3 + √5

Hence, option (c).

» Your doubt will be displayed only after approval.