Solve 3sqrt{8}-4sqrt{32}+5sqrt{128}

$$3 \sqrt{ 8 } -4 \sqrt{ 32 } +5 \sqrt{ 128 }$$

Evaluate

$$30\sqrt{2}\approx 42.426406871$$

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}.

$$3\times 2\sqrt{2}-4\sqrt{32}+5\sqrt{128}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}-4\sqrt{32}+5\sqrt{128}$$

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}.

$$6\sqrt{2}-4\times 4\sqrt{2}+5\sqrt{128}$$

Multiply -4 and 4 to get -16.

$$6\sqrt{2}-16\sqrt{2}+5\sqrt{128}$$

Combine 6\sqrt{2} and -16\sqrt{2} to get -10\sqrt{2}.

$$-10\sqrt{2}+5\sqrt{128}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$-10\sqrt{2}+5\times 8\sqrt{2}$$

Multiply 5 and 8 to get 40.

$$-10\sqrt{2}+40\sqrt{2}$$

Combine -10\sqrt{2} and 40\sqrt{2} to get 30\sqrt{2}.

$$30\sqrt{2}$$