Solve (4-sqrt{11})(-10-sqrt{77})

$$( 4 - \sqrt { 11 } ) ( - 10 - \sqrt { 77 } )$$

Evaluate

$$10\sqrt{11}+11\sqrt{7}-4\sqrt{77}-40\approx -12.830345224$$

Solution Steps

Apply the distributive property by multiplying each term of 4-\sqrt{11} by each term of -10-\sqrt{77}.

$$-40-4\sqrt{77}+10\sqrt{11}+\sqrt{11}\sqrt{77}$$

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}.

$$-40-4\sqrt{77}+10\sqrt{11}+\sqrt{11}\sqrt{11}\sqrt{7}$$

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

$$-40-4\sqrt{77}+10\sqrt{11}+11\sqrt{7}$$