Solve 7*47-(-3)(9)/sqrt{7*37-9sqrt{7*95-81}}

$$\frac { 7 \times 47 - ( - 3 ) ( 9 ) } { \sqrt { 7 \times 37 - 9 } \sqrt { 7 \times 95 - 81 } }$$

Evaluate

$$\frac{89\sqrt{365}}{1825}\approx 0.931694582$$

Solution Steps

Multiply 7 and 47 to get 329.

$$\frac{329-\left(-3\times 9\right)}{\sqrt{7\times 37-9}\sqrt{7\times 95-81}}$$

Multiply -3 and 9 to get -27.

$$\frac{329-\left(-27\right)}{\sqrt{7\times 37-9}\sqrt{7\times 95-81}}$$

The opposite of -27 is 27.

$$\frac{329+27}{\sqrt{7\times 37-9}\sqrt{7\times 95-81}}$$

Add 329 and 27 to get 356.

$$\frac{356}{\sqrt{7\times 37-9}\sqrt{7\times 95-81}}$$

Multiply 7 and 37 to get 259.

$$\frac{356}{\sqrt{259-9}\sqrt{7\times 95-81}}$$

Subtract 9 from 259 to get 250.

$$\frac{356}{\sqrt{250}\sqrt{7\times 95-81}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{356}{5\sqrt{10}\sqrt{7\times 95-81}}$$

Multiply 7 and 95 to get 665.

$$\frac{356}{5\sqrt{10}\sqrt{665-81}}$$

Subtract 81 from 665 to get 584.

$$\frac{356}{5\sqrt{10}\sqrt{584}}$$

Factor 584=2^{2}\times 146. Rewrite the square root of the product \sqrt{2^{2}\times 146} as the product of square roots \sqrt{2^{2}}\sqrt{146}. Take the square root of 2^{2}.

$$\frac{356}{5\sqrt{10}\times 2\sqrt{146}}$$

Multiply 5 and 2 to get 10.

$$\frac{356}{10\sqrt{10}\sqrt{146}}$$

To multiply \sqrt{10} and \sqrt{146}, multiply the numbers under the square root.

$$\frac{356}{10\sqrt{1460}}$$

Rationalize the denominator of \frac{356}{10\sqrt{1460}} by multiplying numerator and denominator by \sqrt{1460}.

$$\frac{356\sqrt{1460}}{10\left(\sqrt{1460}\right)^{2}}$$

The square of \sqrt{1460} is 1460.

$$\frac{356\sqrt{1460}}{10\times 1460}$$

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{89\sqrt{1460}}{5\times 730}$$

Factor 1460=2^{2}\times 365. Rewrite the square root of the product \sqrt{2^{2}\times 365} as the product of square roots \sqrt{2^{2}}\sqrt{365}. Take the square root of 2^{2}.

$$\frac{89\times 2\sqrt{365}}{5\times 730}$$

Multiply 89 and 2 to get 178.

$$\frac{178\sqrt{365}}{5\times 730}$$

Multiply 5 and 730 to get 3650.

$$\frac{178\sqrt{365}}{3650}$$

Divide 178\sqrt{365} by 3650 to get \frac{89}{1825}\sqrt{365}.

$$\frac{89}{1825}\sqrt{365}$$