Simplify the expression \(\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\) where x = 2 and y = 3.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 4)

Answer 1

Concept used:

(√a + √b)/(√a - √b) = {(√a + √b) × (√a + √b)}/{(√a - √b) × (√a + √b)}

Formula used:

(a - b)² = a² + b² - 2ab

a2 - b2 = (a + b) × (a - b)

Calculation:

(√x - √y)/(√x + √y)

⇒ {(√x - √y) × (√x - √y)}/{(√x + √y) × (√x - √y)}

⇒ (√x - √y)²/}(√x)² - (√y)²

Now, putting the value of x = 2 and y = 3

⇒ (√2 - √3)2/}(√2)2 - (√3)2

⇒ - {(√2)2 + (√3)2 - 2 × √2 × √3}

⇒ - (2 + 3 - 2√6)

⇒ 2√6 - 5

∴ The correct answer is 2√6 - 5.

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