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

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

Evaluate

$$60\sqrt{15}\approx 232.379000772$$

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}.

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

Cancel out 2 and 2.

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

Multiply 3 and -15 to get -45.

$$-45\sqrt{5}\left(-\frac{1}{3}\right)\sqrt{48}$$

Express -45\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{-45\left(-1\right)}{3}\sqrt{5}\sqrt{48}$$

Multiply -45 and -1 to get 45.

$$\frac{45}{3}\sqrt{5}\sqrt{48}$$

Divide 45 by 3 to get 15.

$$15\sqrt{5}\sqrt{48}$$

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}.

$$15\sqrt{5}\times 4\sqrt{3}$$

Multiply 15 and 4 to get 60.

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

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

$$60\sqrt{15}$$