Solve sqrt{1728/1372}=

$$\sqrt { \frac { 1728 } { 1372 } } =$$

Evaluate

$$\frac{12\sqrt{21}}{49}\approx 1.122263435$$

Solution Steps

Reduce the fraction \frac{1728}{1372} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{432}{343}}$$

Rewrite the square root of the division \sqrt{\frac{432}{343}} as the division of square roots \frac{\sqrt{432}}{\sqrt{343}}.

$$\frac{\sqrt{432}}{\sqrt{343}}$$

Factor 432=12^{2}\times 3. Rewrite the square root of the product \sqrt{12^{2}\times 3} as the product of square roots \sqrt{12^{2}}\sqrt{3}. Take the square root of 12^{2}.

$$\frac{12\sqrt{3}}{\sqrt{343}}$$

Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.

$$\frac{12\sqrt{3}}{7\sqrt{7}}$$

Rationalize the denominator of \frac{12\sqrt{3}}{7\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{12\sqrt{3}\sqrt{7}}{7\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{12\sqrt{3}\sqrt{7}}{7\times 7}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{12\sqrt{21}}{7\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{12\sqrt{21}}{49}$$