Solve (3+sqrt{11})sqrt{10-3}sqrt{11}

$$( 3 + \sqrt { 11 } ) \sqrt { 10 - 3 } \sqrt { 11 }$$

Evaluate

$$3\sqrt{77}+11\sqrt{7}\approx 55.428157584$$

Solution Steps

Subtract 3 from 10 to get 7.

$$\left(3+\sqrt{11}\right)\sqrt{7}\sqrt{11}$$

To multiply \sqrt{7} and \sqrt{11}, multiply the numbers under the square root.

$$\left(3+\sqrt{11}\right)\sqrt{77}$$

Use the distributive property to multiply 3+\sqrt{11} by \sqrt{77}.

$$3\sqrt{77}+\sqrt{11}\sqrt{77}$$

Factor 77=11\times 7. Rewrite the square root of the product \sqrt{11\times 7} as the product of square roots \sqrt{11}\sqrt{7}.

$$3\sqrt{77}+\sqrt{11}\sqrt{11}\sqrt{7}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$3\sqrt{77}+11\sqrt{7}$$