Solve 2sqrt{11}(3sqrt{2}-sqrt{50}+3sqrt{32})

$$2 \sqrt { 11 } ( 3 \sqrt { 2 } - \sqrt { 50 } + 3 \sqrt { 32 } )$$

Evaluate

$$20\sqrt{22}\approx 93.808315196$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{11}\left(3\sqrt{2}-5\sqrt{2}+3\sqrt{32}\right)$$

Combine 3\sqrt{2} and -5\sqrt{2} to get -2\sqrt{2}.

$$2\sqrt{11}\left(-2\sqrt{2}+3\sqrt{32}\right)$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$2\sqrt{11}\left(-2\sqrt{2}+3\times 4\sqrt{2}\right)$$

Multiply 3 and 4 to get 12.

$$2\sqrt{11}\left(-2\sqrt{2}+12\sqrt{2}\right)$$

Combine -2\sqrt{2} and 12\sqrt{2} to get 10\sqrt{2}.

$$2\sqrt{11}\times 10\sqrt{2}$$

Multiply 2 and 10 to get 20.

$$20\sqrt{11}\sqrt{2}$$

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$20\sqrt{22}$$