Solve frac{5sqrt{7}*sqrt{3}}{sqrt{28}}

$$\frac { 5 \sqrt { 7 } \times \sqrt { 3 } } { \sqrt { 28 } }$$

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

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

$$\frac{5\sqrt{21}}{\sqrt{28}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{5\sqrt{21}}{2\sqrt{7}}$$

Rationalize the denominator of \frac{5\sqrt{21}}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{5\sqrt{21}\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{5\sqrt{21}\sqrt{7}}{2\times 7}$$

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$\frac{5\sqrt{7}\sqrt{3}\sqrt{7}}{2\times 7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{5\times 7\sqrt{3}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{5\times 7\sqrt{3}}{14}$$

Multiply 5 and 7 to get 35.

$$\frac{35\sqrt{3}}{14}$$

Divide 35\sqrt{3} by 14 to get \frac{5}{2}\sqrt{3}.

$$\frac{5}{2}\sqrt{3}$$