Question

write the following surds in exponential form. (a) 5root9 (b)3root43 (c)3root4root14 (d)3root343 (e)4root1225​

Answer 1

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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