Solve {left(77/89xsqrt{45(6)2}right)}^2

$${ \left(7 \frac{ 7 }{ 89x \sqrt{ 45(6)2 } } \right) }^{ 2 }$$

Evaluate

$$\frac{2401}{4277340x^{2}}$$

Solution Steps

Multiply 45 and 6 to get 270.

$$\left(7\times \frac{7}{89x\sqrt{270\times 2}}\right)^{2}$$

Multiply 270 and 2 to get 540.

$$\left(7\times \frac{7}{89x\sqrt{540}}\right)^{2}$$

Factor 540=6^{2}\times 15. Rewrite the square root of the product \sqrt{6^{2}\times 15} as the product of square roots \sqrt{6^{2}}\sqrt{15}. Take the square root of 6^{2}.

$$\left(7\times \frac{7}{89x\times 6\sqrt{15}}\right)^{2}$$

Multiply 89 and 6 to get 534.

$$\left(7\times \frac{7}{534x\sqrt{15}}\right)^{2}$$

Rationalize the denominator of \frac{7}{534x\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\left(7\times \frac{7\sqrt{15}}{534x\left(\sqrt{15}\right)^{2}}\right)^{2}$$

The square of \sqrt{15} is 15.

$$\left(7\times \frac{7\sqrt{15}}{534x\times 15}\right)^{2}$$

Multiply 534 and 15 to get 8010.

$$\left(7\times \frac{7\sqrt{15}}{8010x}\right)^{2}$$

Express 7\times \frac{7\sqrt{15}}{8010x} as a single fraction.

$$\left(\frac{7\times 7\sqrt{15}}{8010x}\right)^{2}$$

To raise \frac{7\times 7\sqrt{15}}{8010x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7\times 7\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Multiply 7 and 7 to get 49.

$$\frac{\left(49\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Expand \left(49\sqrt{15}\right)^{2}.

$$\frac{49^{2}\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{2401\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{2401\times 15}{\left(8010x\right)^{2}}$$

Multiply 2401 and 15 to get 36015.

$$\frac{36015}{\left(8010x\right)^{2}}$$

Expand \left(8010x\right)^{2}.

$$\frac{36015}{8010^{2}x^{2}}$$

Calculate 8010 to the power of 2 and get 64160100.

$$\frac{36015}{64160100x^{2}}$$

Expand

$$\frac{2401}{4277340x^{2}}$$

Solution Steps

Multiply 45 and 6 to get 270.

$$\left(7\times \frac{7}{89x\sqrt{270\times 2}}\right)^{2}$$

Multiply 270 and 2 to get 540.

$$\left(7\times \frac{7}{89x\sqrt{540}}\right)^{2}$$

Factor 540=6^{2}\times 15. Rewrite the square root of the product \sqrt{6^{2}\times 15} as the product of square roots \sqrt{6^{2}}\sqrt{15}. Take the square root of 6^{2}.

$$\left(7\times \frac{7}{89x\times 6\sqrt{15}}\right)^{2}$$

Multiply 89 and 6 to get 534.

$$\left(7\times \frac{7}{534x\sqrt{15}}\right)^{2}$$

Rationalize the denominator of \frac{7}{534x\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\left(7\times \frac{7\sqrt{15}}{534x\left(\sqrt{15}\right)^{2}}\right)^{2}$$

The square of \sqrt{15} is 15.

$$\left(7\times \frac{7\sqrt{15}}{534x\times 15}\right)^{2}$$

Multiply 534 and 15 to get 8010.

$$\left(7\times \frac{7\sqrt{15}}{8010x}\right)^{2}$$

Express 7\times \frac{7\sqrt{15}}{8010x} as a single fraction.

$$\left(\frac{7\times 7\sqrt{15}}{8010x}\right)^{2}$$

To raise \frac{7\times 7\sqrt{15}}{8010x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7\times 7\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Multiply 7 and 7 to get 49.

$$\frac{\left(49\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Expand \left(49\sqrt{15}\right)^{2}.

$$\frac{49^{2}\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{2401\left(\sqrt{15}\right)^{2}}{\left(8010x\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{2401\times 15}{\left(8010x\right)^{2}}$$

Multiply 2401 and 15 to get 36015.

$$\frac{36015}{\left(8010x\right)^{2}}$$

Expand \left(8010x\right)^{2}.

$$\frac{36015}{8010^{2}x^{2}}$$

Calculate 8010 to the power of 2 and get 64160100.

$$\frac{36015}{64160100x^{2}}$$