Solve 3sqrt{2}+4sqrt{64}+4sqrt{2500}+3sqrt{8}

$$3 \sqrt{ 2 } +4 \sqrt{ 64 } +4 \sqrt{ 2500 } +3 \sqrt{ 8 }$$

Evaluate

$$9\sqrt{2}+232\approx 244.727922061$$

Solution Steps

Calculate the square root of 64 and get 8.

$$3\sqrt{2}+4\times 8+4\sqrt{2500}+3\sqrt{8}$$

Multiply 4 and 8 to get 32.

$$3\sqrt{2}+32+4\sqrt{2500}+3\sqrt{8}$$

Calculate the square root of 2500 and get 50.

$$3\sqrt{2}+32+4\times 50+3\sqrt{8}$$

Multiply 4 and 50 to get 200.

$$3\sqrt{2}+32+200+3\sqrt{8}$$

Add 32 and 200 to get 232.

$$3\sqrt{2}+232+3\sqrt{8}$$

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}.

$$3\sqrt{2}+232+3\times 2\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$3\sqrt{2}+232+6\sqrt{2}$$

Combine 3\sqrt{2} and 6\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}+232$$