Question

Simplify. Assume a and b are greater than zero.
√5ab^3/3

Answer 1

To simplify the expression \(\sqrt{\frac{5ab^3}{3}}\), we can break it down as follows:

1. Split the square root into two parts:
\[
\sqrt{\frac{5ab^3}{3}} = \frac{\sqrt{5ab^3}}{\sqrt{3}}
\]

2. Now, simplify the square root of the numerator:
\[
\sqrt{5ab^3} = \sqrt{5} \cdot \sqrt{a} \cdot \sqrt{b^3}
\]

3. Since \(b^3 = b^2 \cdot b\), we can simplify \(\sqrt{b^3}\):
\[
\sqrt{b^3} = \sqrt{b^2 \cdot b} = \sqrt{b^2} \cdot \sqrt{b} = b \cdot \sqrt{b}
\]

4. Combine everything together:
\[
\sqrt{5ab^3} = \sqrt{5} \cdot \sqrt{a} \cdot b \cdot \sqrt{b} = b\sqrt{5a} \cdot \sqrt{b}
\]
Therefore:
\[
\sqrt{5ab^3} = b\sqrt{5ab}
\]

5. Now, put it all back into the expression:
\[
\frac{\sqrt{5ab^3}}{\sqrt{3}} = \frac{b\sqrt{5ab}}{\sqrt{3}}
\]

The final simplified expression is:
\[
\frac{b\sqrt{5ab}}{\sqrt{3}}
\]