Solve frac{sqrt{75}*sqrt{28}}{sqrt{21}}

$$\frac { \sqrt { 75 } \cdot \sqrt { 28 } } { \sqrt { 21 } }$$

Evaluate

$$10$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}\sqrt{28}}{\sqrt{21}}$$

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}.

$$\frac{5\sqrt{3}\times 2\sqrt{7}}{\sqrt{21}}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{3}\sqrt{7}}{\sqrt{21}}$$

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

$$\frac{10\sqrt{21}}{\sqrt{21}}$$

Rationalize the denominator of \frac{10\sqrt{21}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{10\sqrt{21}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{10\sqrt{21}\sqrt{21}}{21}$$

Multiply \sqrt{21} and \sqrt{21} to get 21.

$$\frac{10\times 21}{21}$$

Multiply 10 and 21 to get 210.

$$\frac{210}{21}$$

Divide 210 by 21 to get 10.

$$10$$

Factor

$$2\times 5$$