Square root of Surds — CAT Previous-Year Questions

If (a + b√n) is the positive square root of (29 - 12√5), where a and b are integers, and n is a natural number, then the maximum possible value of (a + b + n) is

If ${\left(x+6\sqrt{2}\right)}^{\frac{1}{2}}$ - ${\left(x-6\sqrt{2}\right)}^{\frac{1}{2}}$ = $2\sqrt{2}$, then x equals

(a + b√3)² = 52 + 30√3, where a and b are natural numbers, then a + b equals

If $\sqrt{5x+9}$ + $\sqrt{5x-9}$ = 3(2 + √2), then find the value of $\sqrt{10x+9}$?

Let x = $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-....to infinity.}}}}$ Then x equals