Solve sqrt{6}*5*sqrt{24}-sqrt{18}divsqrt{2}-sqrt{10816}+sqrt{5}*sqrt{10}*sqrt{2}

$$\sqrt { 6 } \times 5 \times \sqrt { 24 } - \sqrt { 18 } \div \sqrt { 2 } - \sqrt { 10816 } + \sqrt { 5 } \times \sqrt { 10 } \times \sqrt { 2 }$$

Evaluate

$$-37$$

Solution Steps

Factor 24=6\times 4. Rewrite the square root of the product \sqrt{6\times 4} as the product of square roots \sqrt{6}\sqrt{4}.

$$5\sqrt{6}\sqrt{6}\sqrt{4}-\frac{\sqrt{18}}{\sqrt{2}}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$5\times 6\sqrt{4}-\frac{\sqrt{18}}{\sqrt{2}}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Multiply 5 and 6 to get 30.

$$30\sqrt{4}-\frac{\sqrt{18}}{\sqrt{2}}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Calculate the square root of 4 and get 2.

$$30\times 2-\frac{\sqrt{18}}{\sqrt{2}}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Multiply 30 and 2 to get 60.

$$60-\frac{\sqrt{18}}{\sqrt{2}}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Rewrite the division of square roots \frac{\sqrt{18}}{\sqrt{2}} as the square root of the division \sqrt{\frac{18}{2}} and perform the division.

$$60-\sqrt{9}-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Calculate the square root of 9 and get 3.

$$60-3-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Subtract 3 from 60 to get 57.

$$57-\sqrt{10816}+\sqrt{5}\sqrt{10}\sqrt{2}$$

Calculate the square root of 10816 and get 104.

$$57-104+\sqrt{5}\sqrt{10}\sqrt{2}$$

Subtract 104 from 57 to get -47.

$$-47+\sqrt{5}\sqrt{10}\sqrt{2}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$-47+\sqrt{5}\sqrt{5}\sqrt{2}\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$-47+5\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$-47+5\times 2$$

Multiply 5 and 2 to get 10.

$$-47+10$$

Add -47 and 10 to get -37.

$$-37$$

Factor

$$-37$$