Solve sqrt{0.6/0.3^2*7.69}

$$\sqrt { \frac { 0.6 } { 0.3 ^ { 2 } \times 7.69 } }$$

Evaluate

$$\frac{20\sqrt{11535}}{2307}\approx 0.93108901$$

Solution Steps

Calculate 0.3 to the power of 2 and get 0.09.

$$\sqrt{\frac{0.6}{0.09\times 7.69}}$$

Multiply 0.09 and 7.69 to get 0.6921.

$$\sqrt{\frac{0.6}{0.6921}}$$

Expand \frac{0.6}{0.6921} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{6000}{6921}}$$

Reduce the fraction \frac{6000}{6921} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{2000}{2307}}$$

Rewrite the square root of the division \sqrt{\frac{2000}{2307}} as the division of square roots \frac{\sqrt{2000}}{\sqrt{2307}}.

$$\frac{\sqrt{2000}}{\sqrt{2307}}$$

Factor 2000=20^{2}\times 5. Rewrite the square root of the product \sqrt{20^{2}\times 5} as the product of square roots \sqrt{20^{2}}\sqrt{5}. Take the square root of 20^{2}.

$$\frac{20\sqrt{5}}{\sqrt{2307}}$$

Rationalize the denominator of \frac{20\sqrt{5}}{\sqrt{2307}} by multiplying numerator and denominator by \sqrt{2307}.

$$\frac{20\sqrt{5}\sqrt{2307}}{\left(\sqrt{2307}\right)^{2}}$$

The square of \sqrt{2307} is 2307.

$$\frac{20\sqrt{5}\sqrt{2307}}{2307}$$

To multiply \sqrt{5} and \sqrt{2307}, multiply the numbers under the square root.

$$\frac{20\sqrt{11535}}{2307}$$