​ Use the binomial theorem to evaluate the following upto four places of decimals. 4√16.08 ​

Question

Use the binomial theorem to evaluate the following upto four places of decimals.

\(\sqrt[4]{16.08}\)

 4√16.08

Answer 1

\(\sqrt[4]{16.08}\)

 = (16 + 0.08)^1/4

 = [16(1 + 0.005)]^1/4

 = 16^1/4 (1 + 0.005)^1/4

 = 2 [1 + 0.00125 - 0.0000023 + ...]

 = 2(1.0012477)

 = 2.0024954

 = 2.0025