Question

evaluate the expression \\(\sqrt3{125^2}\\).

enter your answer as the correct value, like this: 42

Explanation:

Step1: Rewrite using rational exponents

$$\sqrt[3]{125^2} = (125^2)^{\frac{1}{3}} = 125^{\frac{2}{3}}$$

Step2: Express the base as a power

$$125 = 5^3$$

Step3: Simplify the exponent

$$(5^3)^{\frac{2}{3}} = 5^{3 \times \frac{2}{3}} = 5^2$$

Step4: Calculate the final value

$$5^2 = 25$$

Answer:

25