Square root of Surds — CAT Previous-Year Questions

5 previous-year questions on Square root of Surds from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.

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5 questions

Square root of Surds · CAT PYQs

CAT 2024 Slot 1 · QA

Q1.

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

CAT 2024 Slot 2 · QA

Q2.

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

CAT 2024 Slot 3 · QA

Q3.

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

CAT 2023 Slot 1 · QA

Q4.

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

CAT 2005 · QA

Passage / Data

Answer the next 2 questions based on the information given below.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Q5.

Let x = $\sqrt{4 + \sqrt{4 - \sqrt{4 + \sqrt{4 - . . . . t o i n f i n i t y .}}}}$ Then x equals