Solve frac{21sqrt{15}}{18sqrt{12}}

$$\frac { 21 \sqrt { 15 } } { 18 \sqrt { 12 } }$$

Evaluate

$$\frac{7\sqrt{5}}{12}\approx 1.304372987$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{7\sqrt{15}}{6\sqrt{12}}$$

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}.

$$\frac{7\sqrt{15}}{6\times 2\sqrt{3}}$$

Multiply 6 and 2 to get 12.

$$\frac{7\sqrt{15}}{12\sqrt{3}}$$

Rationalize the denominator of \frac{7\sqrt{15}}{12\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{7\sqrt{15}\sqrt{3}}{12\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{7\sqrt{15}\sqrt{3}}{12\times 3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{7\sqrt{3}\sqrt{5}\sqrt{3}}{12\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{7\times 3\sqrt{5}}{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{7\times 3\sqrt{5}}{36}$$

Multiply 7 and 3 to get 21.

$$\frac{21\sqrt{5}}{36}$$

Divide 21\sqrt{5} by 36 to get \frac{7}{12}\sqrt{5}.

$$\frac{7}{12}\sqrt{5}$$