Solve 9sqrt{8}+3sqrt{2}-16sqrt{32}

$$9 \sqrt { 8 } + 3 \sqrt { 2 } - 16 \sqrt { 32 }$$

Evaluate

$$-43\sqrt{2}\approx -60.811183182$$

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}.

$$9\times 2\sqrt{2}+3\sqrt{2}-16\sqrt{32}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{2}+3\sqrt{2}-16\sqrt{32}$$

Combine 18\sqrt{2} and 3\sqrt{2} to get 21\sqrt{2}.

$$21\sqrt{2}-16\sqrt{32}$$

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}.

$$21\sqrt{2}-16\times 4\sqrt{2}$$

Multiply -16 and 4 to get -64.

$$21\sqrt{2}-64\sqrt{2}$$

Combine 21\sqrt{2} and -64\sqrt{2} to get -43\sqrt{2}.

$$-43\sqrt{2}$$