Question

what is the value of the expression \\(\sqrt4{25^2}\\)?\\(\sqrt4{25^2} = \square\\)(type an integer or a decimal.)

Explanation:

Step1: Rewrite the expression using exponents

Recall that the \(n\)-th root of a number \(a\) can be written as \(a^{\frac{1}{n}}\), and \((a^m)^n=a^{mn}\). So, \(\sqrt[4]{25^2}=(25^2)^{\frac{1}{4}}\).

Step2: Simplify the exponent

Using the power - of - a - power rule \((a^m)^n = a^{mn}\), we have \((25^2)^{\frac{1}{4}}=25^{\frac{2}{4}}=25^{\frac{1}{2}}\).

Step3: Evaluate the expression

We know that \(a^{\frac{1}{2}}=\sqrt{a}\), so \(25^{\frac{1}{2}}=\sqrt{25} = 5\).

Answer:

5