Solve sqrt{(7-0,6):7,1}-7/4+1,2^2

$$\sqrt { ( 7 - 0,6 ) : 7,1 } - \frac { 7 } { 4 } + 1,2 ^ { 2 }$$

Evaluate

$$\frac{8\sqrt{71}}{71}+2,25\approx 3.199425327$$

Short Solution Steps

Subtract 0,6 from 7 to get 6,4.

$$\sqrt{\frac{6,4}{7,1}}-\frac{7}{4}+1\times 2^{2}$$

Expand \frac{6,4}{7,1} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{64}{71}}-\frac{7}{4}+1\times 2^{2}$$

Rewrite the square root of the division \sqrt{\frac{64}{71}} as the division of square roots \frac{\sqrt{64}}{\sqrt{71}}.

$$\frac{\sqrt{64}}{\sqrt{71}}-\frac{7}{4}+1\times 2^{2}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{\sqrt{71}}-\frac{7}{4}+1\times 2^{2}$$

Rationalize the denominator of \frac{8}{\sqrt{71}} by multiplying numerator and denominator by \sqrt{71}.

$$\frac{8\sqrt{71}}{\left(\sqrt{71}\right)^{2}}-\frac{7}{4}+1\times 2^{2}$$

The square of \sqrt{71} is 71.

$$\frac{8\sqrt{71}}{71}-\frac{7}{4}+1\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{8\sqrt{71}}{71}-\frac{7}{4}+1\times 4$$

Multiply 1 and 4 to get 4.

$$\frac{8\sqrt{71}}{71}-\frac{7}{4}+4$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{8\sqrt{71}}{71}-\frac{7}{4}+\frac{16}{4}$$

Since -\frac{7}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{8\sqrt{71}}{71}+\frac{-7+16}{4}$$

Add -7 and 16 to get 9.

$$\frac{8\sqrt{71}}{71}+\frac{9}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 71 and 4 is 284. Multiply \frac{8\sqrt{71}}{71} times \frac{4}{4}. Multiply \frac{9}{4} times \frac{71}{71}.

$$\frac{4\times 8\sqrt{71}}{284}+\frac{9\times 71}{284}$$

Since \frac{4\times 8\sqrt{71}}{284} and \frac{9\times 71}{284} have the same denominator, add them by adding their numerators.

$$\frac{4\times 8\sqrt{71}+9\times 71}{284}$$

Do the multiplications in 4\times 8\sqrt{71}+9\times 71.

$$\frac{32\sqrt{71}+639}{284}$$

Factor

$$\frac{32 \sqrt{71} + 639}{284} = 3.1994253265550827$$