Solve sqrt{12}divfrac{sqrt{12}}{3}

$$\sqrt{ 12 } \div \frac{ \sqrt{ 12 } }{ 3 }$$

Evaluate

$$3$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\frac{\sqrt{12}}{3}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\frac{2\sqrt{3}}{3}}$$

Divide 2\sqrt{3} by \frac{2\sqrt{3}}{3} by multiplying 2\sqrt{3} by the reciprocal of \frac{2\sqrt{3}}{3}.

$$\frac{2\sqrt{3}\times 3}{2\sqrt{3}}$$

Cancel out 2\sqrt{3} in both numerator and denominator.

$$3$$

Factor

$$3$$