Solve 5*1500-70*100/sqrt{5*1150-70^2sqrt{5*2200-100^2}}

$$\frac{ 5 \times 1500-70 \times 100 }{ \sqrt{ 5 \times 1150- { 70 }^{ 2 } } \sqrt{ 5 \times 2200- { 100 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{85}}{17}\approx 0.542326145$$

Solution Steps

Multiply 5 and 1500 to get 7500.

$$\frac{7500-70\times 100}{\sqrt{5\times 1150-70^{2}}\sqrt{5\times 2200-100^{2}}}$$

Multiply 70 and 100 to get 7000.

$$\frac{7500-7000}{\sqrt{5\times 1150-70^{2}}\sqrt{5\times 2200-100^{2}}}$$

Subtract 7000 from 7500 to get 500.

$$\frac{500}{\sqrt{5\times 1150-70^{2}}\sqrt{5\times 2200-100^{2}}}$$

Multiply 5 and 1150 to get 5750.

$$\frac{500}{\sqrt{5750-70^{2}}\sqrt{5\times 2200-100^{2}}}$$

Calculate 70 to the power of 2 and get 4900.

$$\frac{500}{\sqrt{5750-4900}\sqrt{5\times 2200-100^{2}}}$$

Subtract 4900 from 5750 to get 850.

$$\frac{500}{\sqrt{850}\sqrt{5\times 2200-100^{2}}}$$

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}.

$$\frac{500}{5\sqrt{34}\sqrt{5\times 2200-100^{2}}}$$

Multiply 5 and 2200 to get 11000.

$$\frac{500}{5\sqrt{34}\sqrt{11000-100^{2}}}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{500}{5\sqrt{34}\sqrt{11000-10000}}$$

Subtract 10000 from 11000 to get 1000.

$$\frac{500}{5\sqrt{34}\sqrt{1000}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{500}{5\sqrt{34}\times 10\sqrt{10}}$$

Multiply 5 and 10 to get 50.

$$\frac{500}{50\sqrt{34}\sqrt{10}}$$

To multiply \sqrt{34} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{500}{50\sqrt{340}}$$

Rationalize the denominator of \frac{500}{50\sqrt{340}} by multiplying numerator and denominator by \sqrt{340}.

$$\frac{500\sqrt{340}}{50\left(\sqrt{340}\right)^{2}}$$

The square of \sqrt{340} is 340.

$$\frac{500\sqrt{340}}{50\times 340}$$

Cancel out 10\times 50 in both numerator and denominator.

$$\frac{\sqrt{340}}{34}$$

Factor 340=2^{2}\times 85. Rewrite the square root of the product \sqrt{2^{2}\times 85} as the product of square roots \sqrt{2^{2}}\sqrt{85}. Take the square root of 2^{2}.

$$\frac{2\sqrt{85}}{34}$$

Divide 2\sqrt{85} by 34 to get \frac{1}{17}\sqrt{85}.

$$\frac{1}{17}\sqrt{85}$$