Solve sqrt{5}+12sqrt{8}-3sqrt{5}+4sqrt{8}

$$\sqrt { 5 } + 12 \sqrt { 8 } - 3 \sqrt { 5 } + 4 \sqrt { 8 }$$

Evaluate

$$32\sqrt{2}-2\sqrt{5}\approx 40.782698041$$

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}.

$$\sqrt{5}+12\times 2\sqrt{2}-3\sqrt{5}+4\sqrt{8}$$

Multiply 12 and 2 to get 24.

$$\sqrt{5}+24\sqrt{2}-3\sqrt{5}+4\sqrt{8}$$

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

$$-2\sqrt{5}+24\sqrt{2}+4\sqrt{8}$$

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}.

$$-2\sqrt{5}+24\sqrt{2}+4\times 2\sqrt{2}$$

Multiply 4 and 2 to get 8.

$$-2\sqrt{5}+24\sqrt{2}+8\sqrt{2}$$

Combine 24\sqrt{2} and 8\sqrt{2} to get 32\sqrt{2}.

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