Solve 7sqrt{32}-5sqrt{2}+sqrt{8}

$$7 \sqrt{ 32 } -5 \sqrt{ 2 } + \sqrt{ 8 }$$

Evaluate

$$25\sqrt{2}\approx 35.355339059$$

Solution Steps

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}.

$$7\times 4\sqrt{2}-5\sqrt{2}+\sqrt{8}$$

Multiply 7 and 4 to get 28.

$$28\sqrt{2}-5\sqrt{2}+\sqrt{8}$$

Combine 28\sqrt{2} and -5\sqrt{2} to get 23\sqrt{2}.

$$23\sqrt{2}+\sqrt{8}$$

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}.

$$23\sqrt{2}+2\sqrt{2}$$

Combine 23\sqrt{2} and 2\sqrt{2} to get 25\sqrt{2}.

$$25\sqrt{2}$$