Solve frac{5sqrt{72}-3sqrt{8}}{7sqrt{2}}

$$\frac { 5 \sqrt { 72 } - 3 \sqrt { 8 } } { 7 \sqrt { 2 } }$$

Evaluate

$$\frac{24}{7}\approx 3.428571429$$

Solution Steps

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}.

$$\frac{5\times 6\sqrt{2}-3\sqrt{8}}{7\sqrt{2}}$$

Multiply 5 and 6 to get 30.

$$\frac{30\sqrt{2}-3\sqrt{8}}{7\sqrt{2}}$$

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}.

$$\frac{30\sqrt{2}-3\times 2\sqrt{2}}{7\sqrt{2}}$$

Multiply -3 and 2 to get -6.

$$\frac{30\sqrt{2}-6\sqrt{2}}{7\sqrt{2}}$$

Combine 30\sqrt{2} and -6\sqrt{2} to get 24\sqrt{2}.

$$\frac{24\sqrt{2}}{7\sqrt{2}}$$

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

$$\frac{24}{7}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{7} = 3\frac{3}{7} = 3.4285714285714284$$