To solve the expression \(\sqrt[3]{25 \times 2} \times \sqrt[3]{4 \times 5}\), let's go through it step by step.
1. Calculate the values under the cube roots:
- Evaluate \(25 \times 2\):
[tex]\[
25 \times 2 = 50
\][/tex]
- Evaluate \(4 \times 5\):
[tex]\[
4 \times 5 = 20
\][/tex]
2. Rewrite the expression with these products:
[tex]\[
\sqrt[3]{50} \times \sqrt[3]{20}
\][/tex]
3. Combine the cube roots into a single cube root using the property \(\sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{a \times b}\):
[tex]\[
\sqrt[3]{50 \times 20}
\][/tex]
4. Compute the product inside the cube root:
[tex]\[
50 \times 20 = 1000
\][/tex]
5. Simplify the cube root of 1000:
[tex]\[
\sqrt[3]{1000} = \sqrt[3]{10^3}
\][/tex]
6. Evaluate the cube root:
[tex]\[
\sqrt[3]{10^3} = 10
\][/tex]
Therefore, the final answer is:
[tex]\[
\sqrt[3]{25 \times 2} \times \sqrt[3]{4 \times 5} = 10
\][/tex]
