Solve 25sqrt{6^3x/12^4x}

$$25 \sqrt{ \frac{ { 6 }^{ 3 } x }{ { 12 }^{ 4 } x } }$$

Evaluate

$$\frac{25\sqrt{6}}{24}\approx 2.551551815$$

Solution Steps

Cancel out x in both numerator and denominator.

$$25\sqrt{\frac{6^{3}}{12^{4}}}$$

Calculate 6 to the power of 3 and get 216.

$$25\sqrt{\frac{216}{12^{4}}}$$

Calculate 12 to the power of 4 and get 20736.

$$25\sqrt{\frac{216}{20736}}$$

Reduce the fraction \frac{216}{20736} to lowest terms by extracting and canceling out 216.

$$25\sqrt{\frac{1}{96}}$$

Rewrite the square root of the division \sqrt{\frac{1}{96}} as the division of square roots \frac{\sqrt{1}}{\sqrt{96}}.

$$25\times \frac{\sqrt{1}}{\sqrt{96}}$$

Calculate the square root of 1 and get 1.

$$25\times \frac{1}{\sqrt{96}}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$25\times \frac{1}{4\sqrt{6}}$$

Rationalize the denominator of \frac{1}{4\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$25\times \frac{\sqrt{6}}{4\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$25\times \frac{\sqrt{6}}{4\times 6}$$

Multiply 4 and 6 to get 24.

$$25\times \frac{\sqrt{6}}{24}$$

Express 25\times \frac{\sqrt{6}}{24} as a single fraction.

$$\frac{25\sqrt{6}}{24}$$