Solve sqrt{144}*sqrt{1/2}

$$\sqrt{ 144 } \times \sqrt{ \frac{ 1 }{ 2 } }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Calculate the square root of 144 and get 12.

$$12\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$12\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$12\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$12\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$12\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 12 and 2.

$$6\sqrt{2}$$