Question:
Simplify: (√5)^8 ÷ (√5)^2 = 5^n. Find n.
सरल कीजिए: (√5)^8 ÷ (√5)^2 = 5^n. n का मान ज्ञात कीजिए।
Options:
- a) 3
- b) 4
- c) 6
- d) 5
- a) 3
- b) 4
- c) 6
- d) 5
correct answer : a)
Explanation:
(√5)^8 ÷ (√5)^2 = (√5)^(8-2) = (√5)^6
Since √5 = 5^(1/2):
(√5)^6 = (5^(1/2))^6 = 5^3.
Given, 5^3 = 5^n => n = 3.
(√5)^8 ÷ (√5)^2 = (√5)^(8-2) = (√5)^6
चूंकि √5 = 5^(1/2):
(√5)^6 = (5^(1/2))^6 = 5^3.
दिया गया है, 5^3 = 5^n => n = 3.