Chapter 7.4, Problem 41PPS

To determine

To simplify the expression $\sqrt{4c^3{d}^3}\cdot \sqrt{8c^{3}d}$ .

Answer to Problem 41PPS

  $4\cdot \sqrt{2}\cdot c^3\cdot d^2$

Explanation of Solution

Given:

  $\sqrt{4c^3{d}^3}\cdot \sqrt{8c^{3}d}$

Formula used:

The radical rules:

  $\sqrt[n]{a}=a^{\frac{1}{n}}$

  ${(a^m)}^n=a^{mn}$

  $\sqrt[a]{b\times c}=\sqrt[a]{b}\times \sqrt[a]{c}$

Calculation:

Conclusion:

The simplified form of the given expression is equal to $4\cdot \sqrt{2}\cdot c^3\cdot d^2$ .