Solve 3/2sqrt{10}*(1+7)*(-1/3sqrt{48})

$$\frac { 3 } { 2 } \sqrt { 10 } \times ( 1 + 7 ) \times ( - \frac { 1 } { 3 } \sqrt { 48 } )$$

Evaluate

$$-16\sqrt{30}\approx -87.635609201$$

Solution Steps

Add 1 and 7 to get 8.

$$\frac{3}{2}\sqrt{10}\times 8\left(-\frac{1}{3}\right)\sqrt{48}$$

Express \frac{3}{2}\times 8 as a single fraction.

$$\frac{3\times 8}{2}\sqrt{10}\left(-\frac{1}{3}\right)\sqrt{48}$$

Multiply 3 and 8 to get 24.

$$\frac{24}{2}\sqrt{10}\left(-\frac{1}{3}\right)\sqrt{48}$$

Divide 24 by 2 to get 12.

$$12\sqrt{10}\left(-\frac{1}{3}\right)\sqrt{48}$$

Express 12\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{12\left(-1\right)}{3}\sqrt{10}\sqrt{48}$$

Multiply 12 and -1 to get -12.

$$\frac{-12}{3}\sqrt{10}\sqrt{48}$$

Divide -12 by 3 to get -4.

$$-4\sqrt{10}\sqrt{48}$$

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}.

$$-4\sqrt{10}\times 4\sqrt{3}$$

Multiply -4 and 4 to get -16.

$$-16\sqrt{10}\sqrt{3}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$-16\sqrt{30}$$