Question

use the product rule to multiply.
\sqrt3{25} \cdot \sqrt3{5}
\sqrt3{25} \cdot \sqrt3{5} = \square
(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Recall the product rule for radicals

The product rule for cube roots states that \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a \cdot b}\) for real numbers \(a\) and \(b\).
So, for \(\sqrt[3]{25}\cdot\sqrt[3]{5}\), we can apply this rule: \(\sqrt[3]{25}\cdot\sqrt[3]{5}=\sqrt[3]{25\times5}\)

Step2: Simplify the product inside the cube root

Calculate \(25\times5 = 125\). Then we have \(\sqrt[3]{125}\)

Step3: Evaluate the cube root

We know that \(5^3=125\), so \(\sqrt[3]{125} = 5\)

Answer:

\(5\)