Question:
Simplify: \(\dfrac{64^{1/2} \times (1/8)^{-1/3}}{(\sqrt{18} + \sqrt{8})^2 – (\sqrt{18} – \sqrt{8})^2}\)
सरल कीजिए: \(\dfrac{64^{1/2} \times (1/8)^{-1/3}}{(\sqrt{18} + \sqrt{8})^2 – (\sqrt{18} – \sqrt{8})^2}\)
Options:
- 16/3
- 1/3
- 48/12
- 64/15
- 16/3
- 1/3
- 48/12
- 64/15
Correct Answer: b)
Explanation:
Numerator: \(64^{1/2} = 8\) and \((1/8)^{-1/3} = 8^{1/3} = 2 \implies 8 \times 2 = 16\).
Denominator: \((a + b)^2 – (a – b)^2 = 4ab = 4 \times \sqrt{18} \times \sqrt{8} = 4 \times \sqrt{144} = 4 \times 12 = 48\).
Fraction = \(\dfrac{16}{48} = \dfrac{1}{3}\).
अंश = \(8 \times 2 = 16\)।
हर = \(4ab = 4 \times \sqrt{18 \times 8} = 4 \times 12 = 48\)।
भिन्न = \(\dfrac{16}{48} = \dfrac{1}{3}\)।