Question

 What is the value of \(\dfrac{1}{\sqrt{3}-2}\times\dfrac{1}{\sqrt{3}+2}\times\dfrac{1}{\sqrt{5}+\sqrt{6}}\times\dfrac{1}{\sqrt{5}-\sqrt{6}}\)
1. √12 - √17
2. 1
3. 2
4. √12 + √14

Answer 1

Correct Answer - Option 2 : 1

Given:

\(\dfrac{1}{√{3}-2}×\dfrac{1}{√{3}+2}×\dfrac{1}{√{5}+√{6}}×\dfrac{1}{√{5}-√{6}}\)

Formula used:

(a - b)(a + b) = a² - b²

Calculation:

According to the question,

⇒ \(\dfrac{1}{√{3}-2}×\dfrac{1}{√{3}+2}×\dfrac{1}{√{5}+√{6}}×\dfrac{1}{√{5}-√{6}}\)

⇒ {1/(√3² - 2²)} × {1/{√5² - √6²}}

⇒ 1/-1 × 1/-1

⇒ 1

∴ The value of \(\dfrac{1}{\sqrt{3}-2}\times\dfrac{1}{\sqrt{3}+2}\times\dfrac{1}{\sqrt{5}+\sqrt{6}}\times\dfrac{1}{\sqrt{5}-\sqrt{6}}\) is 1.