Solve 25*51-25/2*19/sqrt{20}

$$\frac { 25 \cdot 51 - 25 } { 2 \cdot 19 / \sqrt { 20 } }$$

Evaluate

$$\frac{1250\sqrt{5}}{19}\approx 147.109735362$$

Solution Steps

Multiply 25 and 51 to get 1275.

$$\frac{1275-25}{\frac{2\times 19}{\sqrt{20}}}$$

Subtract 25 from 1275 to get 1250.

$$\frac{1250}{\frac{2\times 19}{\sqrt{20}}}$$

Multiply 2 and 19 to get 38.

$$\frac{1250}{\frac{38}{\sqrt{20}}}$$

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

$$\frac{1250}{\frac{38}{2\sqrt{5}}}$$

Rationalize the denominator of \frac{38}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{1250}{\frac{38\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{1250}{\frac{38\sqrt{5}}{2\times 5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1250}{\frac{19\sqrt{5}}{5}}$$

Divide 1250 by \frac{19\sqrt{5}}{5} by multiplying 1250 by the reciprocal of \frac{19\sqrt{5}}{5}.

$$\frac{1250\times 5}{19\sqrt{5}}$$

Rationalize the denominator of \frac{1250\times 5}{19\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{1250\times 5\sqrt{5}}{19\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{1250\times 5\sqrt{5}}{19\times 5}$$

Multiply 1250 and 5 to get 6250.

$$\frac{6250\sqrt{5}}{19\times 5}$$

Multiply 19 and 5 to get 95.

$$\frac{6250\sqrt{5}}{95}$$

Divide 6250\sqrt{5} by 95 to get \frac{1250}{19}\sqrt{5}.

$$\frac{1250}{19}\sqrt{5}$$