Solve (6sqrt{8}-sqrt{98})+(5sqrt{18}-6sqrt{32})

$$( 6 \sqrt { 8 } - \sqrt { 98 } ) + ( 5 \sqrt { 18 } - 6 \sqrt { 32 } )$$

Evaluate

$$-4\sqrt{2}\approx -5.656854249$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$6\times 2\sqrt{2}-\sqrt{98}+5\sqrt{18}-6\sqrt{32}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{2}-\sqrt{98}+5\sqrt{18}-6\sqrt{32}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$12\sqrt{2}-7\sqrt{2}+5\sqrt{18}-6\sqrt{32}$$

Combine 12\sqrt{2} and -7\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+5\sqrt{18}-6\sqrt{32}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$5\sqrt{2}+5\times 3\sqrt{2}-6\sqrt{32}$$

Multiply 5 and 3 to get 15.

$$5\sqrt{2}+15\sqrt{2}-6\sqrt{32}$$

Combine 5\sqrt{2} and 15\sqrt{2} to get 20\sqrt{2}.

$$20\sqrt{2}-6\sqrt{32}$$

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}.

$$20\sqrt{2}-6\times 4\sqrt{2}$$

Multiply -6 and 4 to get -24.

$$20\sqrt{2}-24\sqrt{2}$$

Combine 20\sqrt{2} and -24\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}$$