Solve 3/2sqrt{20*(-15)*(-1/3sqrt{48})}

$$\frac { 3 } { 2 \sqrt { 20 } \cdot ( - 15 ) \cdot ( - \frac { 1 } { 3 } \sqrt { 48 } ) }$$

Evaluate

$$\frac{\sqrt{15}}{400}\approx 0.009682458$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{3}{2\times 2\sqrt{5}\left(-15\right)\left(-\frac{1}{3}\right)\sqrt{48}}$$

Multiply 2 and 2 to get 4.

$$\frac{3}{4\sqrt{5}\left(-15\right)\left(-\frac{1}{3}\right)\sqrt{48}}$$

Multiply 4 and -15 to get -60.

$$\frac{3}{-60\sqrt{5}\left(-\frac{1}{3}\right)\sqrt{48}}$$

Express -60\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{3}{\frac{-60\left(-1\right)}{3}\sqrt{5}\sqrt{48}}$$

Multiply -60 and -1 to get 60.

$$\frac{3}{\frac{60}{3}\sqrt{5}\sqrt{48}}$$

Divide 60 by 3 to get 20.

$$\frac{3}{20\sqrt{5}\sqrt{48}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{3}{20\sqrt{5}\times 4\sqrt{3}}$$

Multiply 20 and 4 to get 80.

$$\frac{3}{80\sqrt{5}\sqrt{3}}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{3}{80\sqrt{15}}$$

Rationalize the denominator of \frac{3}{80\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{3\sqrt{15}}{80\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{3\sqrt{15}}{80\times 15}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{15}}{5\times 80}$$

Multiply 5 and 80 to get 400.

$$\frac{\sqrt{15}}{400}$$