Solve frac{6.2sqrt{32}+4sqrt{8}}{2sqrt{72}+sqrt{128}}

$$\frac { 6.2 \sqrt { 32 } + 4 \sqrt { 8 } } { 2 \sqrt { 72 } + \sqrt { 128 } }$$

Evaluate

$$1.64$$

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}.

$$\frac{6.2\times 4\sqrt{2}+4\sqrt{8}}{2\sqrt{72}+\sqrt{128}}$$

Multiply 6.2 and 4 to get 24.8.

$$\frac{24.8\sqrt{2}+4\sqrt{8}}{2\sqrt{72}+\sqrt{128}}$$

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}.

$$\frac{24.8\sqrt{2}+4\times 2\sqrt{2}}{2\sqrt{72}+\sqrt{128}}$$

Multiply 4 and 2 to get 8.

$$\frac{24.8\sqrt{2}+8\sqrt{2}}{2\sqrt{72}+\sqrt{128}}$$

Combine 24.8\sqrt{2} and 8\sqrt{2} to get 32.8\sqrt{2}.

$$\frac{32.8\sqrt{2}}{2\sqrt{72}+\sqrt{128}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{32.8\sqrt{2}}{2\times 6\sqrt{2}+\sqrt{128}}$$

Multiply 2 and 6 to get 12.

$$\frac{32.8\sqrt{2}}{12\sqrt{2}+\sqrt{128}}$$

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}.

$$\frac{32.8\sqrt{2}}{12\sqrt{2}+8\sqrt{2}}$$

Combine 12\sqrt{2} and 8\sqrt{2} to get 20\sqrt{2}.

$$\frac{32.8\sqrt{2}}{20\sqrt{2}}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{32.8}{20}$$

Expand \frac{32.8}{20} by multiplying both numerator and the denominator by 10.

$$\frac{328}{200}$$

Reduce the fraction \frac{328}{200} to lowest terms by extracting and canceling out 8.

$$\frac{41}{25}$$

Factor

$$\frac{41}{5 ^ {2}} = 1\frac{16}{25} = 1.64$$