Solve sqrt{128/49}divsqrt{2}

$$\sqrt{ \frac{ 128 }{ 49 } } \div \sqrt{ 2 }$$

Evaluate

$$\frac{8}{7}\approx 1.142857143$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{128}{49}} as the division of square roots \frac{\sqrt{128}}{\sqrt{49}}.

$$\frac{\frac{\sqrt{128}}{\sqrt{49}}}{\sqrt{2}}$$

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}.

$$\frac{\frac{8\sqrt{2}}{\sqrt{49}}}{\sqrt{2}}$$

Calculate the square root of 49 and get 7.

$$\frac{\frac{8\sqrt{2}}{7}}{\sqrt{2}}$$

Express \frac{\frac{8\sqrt{2}}{7}}{\sqrt{2}} as a single fraction.

$$\frac{8\sqrt{2}}{7\sqrt{2}}$$

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

$$\frac{8}{7}$$

Factor

$$\frac{2 ^ {3}}{7} = 1\frac{1}{7} = 1.1428571428571428$$