Solve A=frac{sqrt{56}}{sqrt{21}}

$$A = \frac{ \sqrt{ 56 } }{ \sqrt{ 21 } }$$

Solve for A

$$A = \frac{2 \sqrt{6}}{3} \approx 1.632993162$$

Steps for Solving Linear Equation

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$A=\frac{2\sqrt{14}}{\sqrt{21}}$$

Rationalize the denominator of \frac{2\sqrt{14}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$A=\frac{2\sqrt{14}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$A=\frac{2\sqrt{14}\sqrt{21}}{21}$$

To multiply \sqrt{14} and \sqrt{21}, multiply the numbers under the square root.

$$A=\frac{2\sqrt{294}}{21}$$

Factor 294=7^{2}\times 6. Rewrite the square root of the product \sqrt{7^{2}\times 6} as the product of square roots \sqrt{7^{2}}\sqrt{6}. Take the square root of 7^{2}.

$$A=\frac{2\times 7\sqrt{6}}{21}$$

Multiply 2 and 7 to get 14.

$$A=\frac{14\sqrt{6}}{21}$$

Divide 14\sqrt{6} by 21 to get \frac{2}{3}\sqrt{6}.

$$A=\frac{2}{3}\sqrt{6}$$

Assign A

$$A≔\frac{2\sqrt{6}}{3}$$