write the following surds in exponential form. (a) 5root9 (b)3root43 (c)3root4root14 (d)3root343 (e)4root1225
Answers
Question :- write the following surds in exponential form. (a) 5root9 (b)3root43 (c)3root4root14 (d)3root343 (e)4root1225
Solution :-
a) 5√9
→ 5 * √9
→ 5 * (9)^(1/2)
→ 5 * (3 * 3)^(1/2)
→ 5 * (3²)^(1/2)
using (a^m)^n = a^(m*n)
→ 5 * 3^(2 * 1/2)
→ 5 * 3^1
→ 5 * 3
→ 15.
{ if it is ⁵√9 , than , 9^(1/5) . }
b) ³√43
→ ³√43
using ⁿ√a = (a)^(1/n) ,
→ (43)^(1/3) .
c) ³√4 * √14
→ ³√4 * √14
using ⁿ√a = (a)^(1/n) , and √a = (a)^(1/2), we get,
→ (4)^(1/3) * (14)^(1/2).
d) ³√343
→ ³√343
using ⁿ√a = (a)^(1/n) ,
→ (343)^(1/3)
→ (7³)^(1/3)
using (a^m)^n = a^(m*n)
→ (7)^(3 * 1/3)
→ 7¹
→ 7 .
e) ⁴√(1225)
→ ⁴√1225
using ⁿ√a = (a)^(1/n) ,
→ (1225)^(1/4)
→ (25 * 49)^(1/4)
→ (5² * 7²)^(1/4)
using a^m * b^m = (a * b)^m
→ {(5 * 7)²}^(1/4)
→ (35²)^(1/4)
using (a^m)^n = a^(m*n)
→ (35)^(2 * 1/4)
→ (35)^(1/2).
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