Simplified value of
Question:

Simplified value oi $(25)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$ is

(a) 25

(b) 3

(c) 1

(d) 5

Solution:

$(25)^{\frac{1}{2}} \times 5^{\frac{1}{3}}=\left(5^{2}\right)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$

$=5^{\frac{2}{3}} \times 5^{\frac{1}{3}}$

$=5^{\frac{2}{3}+\frac{1}{3}}$

$=5^{\frac{2+1}{3}}$

$=5^{\frac{3}{3}}$

$=5$

$\therefore$ Simplified value of $(25)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$ is $5 .$

Hence, the correct option is (d).