Solve frac{-12+2sqrt{56}}{2*1/5}

$$\frac{ -12+2 \sqrt{ 56 } }{ 2 \times \frac{ 1 }{ 5 } }$$

Evaluate

$$10\left(\sqrt{14}-3\right)\approx 7.416573868$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{-12+2\times 2\sqrt{14}}{2\times \frac{1}{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{-12+4\sqrt{14}}{2\times \frac{1}{5}}$$

Multiply 2 and \frac{1}{5} to get \frac{2}{5}.

$$\frac{-12+4\sqrt{14}}{\frac{2}{5}}$$

Divide -12+4\sqrt{14} by \frac{2}{5} by multiplying -12+4\sqrt{14} by the reciprocal of \frac{2}{5}.

$$\frac{\left(-12+4\sqrt{14}\right)\times 5}{2}$$

Use the distributive property to multiply -12+4\sqrt{14} by 5.

$$\frac{-60+20\sqrt{14}}{2}$$

Factor

$$10 {(\sqrt{14} - 3)} = 7.416573868$$