Solve 5*470-30*70/sqrt{5*220-30^2sqrt{5*1150-70^2}}

$$\frac { 5 \times 470 - 30 \times 70 } { \sqrt { 5 \times 220 - 30 ^ { 2 } } \sqrt { 5 \times 1150 - 70 ^ { 2 } } }$$

Evaluate

$$\frac{5\sqrt{17}}{34}\approx 0.606339063$$

Solution Steps

Multiply 5 and 470 to get 2350.

$$\frac{2350-30\times 70}{\sqrt{5\times 220-30^{2}}\sqrt{5\times 1150-70^{2}}}$$

Multiply 30 and 70 to get 2100.

$$\frac{2350-2100}{\sqrt{5\times 220-30^{2}}\sqrt{5\times 1150-70^{2}}}$$

Subtract 2100 from 2350 to get 250.

$$\frac{250}{\sqrt{5\times 220-30^{2}}\sqrt{5\times 1150-70^{2}}}$$

Multiply 5 and 220 to get 1100.

$$\frac{250}{\sqrt{1100-30^{2}}\sqrt{5\times 1150-70^{2}}}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{250}{\sqrt{1100-900}\sqrt{5\times 1150-70^{2}}}$$

Subtract 900 from 1100 to get 200.

$$\frac{250}{\sqrt{200}\sqrt{5\times 1150-70^{2}}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{250}{10\sqrt{2}\sqrt{5\times 1150-70^{2}}}$$

Multiply 5 and 1150 to get 5750.

$$\frac{250}{10\sqrt{2}\sqrt{5750-70^{2}}}$$

Calculate 70 to the power of 2 and get 4900.

$$\frac{250}{10\sqrt{2}\sqrt{5750-4900}}$$

Subtract 4900 from 5750 to get 850.

$$\frac{250}{10\sqrt{2}\sqrt{850}}$$

Factor 850=5^{2}\times 34. Rewrite the square root of the product \sqrt{5^{2}\times 34} as the product of square roots \sqrt{5^{2}}\sqrt{34}. Take the square root of 5^{2}.

$$\frac{250}{10\sqrt{2}\times 5\sqrt{34}}$$

Multiply 10 and 5 to get 50.

$$\frac{250}{50\sqrt{2}\sqrt{34}}$$

Factor 34=2\times 17. Rewrite the square root of the product \sqrt{2\times 17} as the product of square roots \sqrt{2}\sqrt{17}.

$$\frac{250}{50\sqrt{2}\sqrt{2}\sqrt{17}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{250}{50\times 2\sqrt{17}}$$

Rationalize the denominator of \frac{250}{50\times 2\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{250\sqrt{17}}{50\times 2\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{250\sqrt{17}}{50\times 2\times 17}$$

Cancel out 50 in both numerator and denominator.

$$\frac{5\sqrt{17}}{2\times 17}$$

Multiply 2 and 17 to get 34.

$$\frac{5\sqrt{17}}{34}$$