Solve frac{sqrt{35}-sqrt{21}}{sqrt{7}}

$$\frac { \sqrt { 35 } - \sqrt { 21 } } { \sqrt { 7 } }$$

Evaluate

$$\sqrt{5}-\sqrt{3}\approx 0.50401717$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{35}-\sqrt{21}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\left(\sqrt{35}-\sqrt{21}\right)\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\left(\sqrt{35}-\sqrt{21}\right)\sqrt{7}}{7}$$

Use the distributive property to multiply \sqrt{35}-\sqrt{21} by \sqrt{7}.

$$\frac{\sqrt{35}\sqrt{7}-\sqrt{21}\sqrt{7}}{7}$$

Factor 35=7\times 5. Rewrite the square root of the product \sqrt{7\times 5} as the product of square roots \sqrt{7}\sqrt{5}.

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

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

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

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}.

$$\frac{7\sqrt{5}-\sqrt{7}\sqrt{3}\sqrt{7}}{7}$$

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

$$\frac{7\sqrt{5}-7\sqrt{3}}{7}$$

Divide each term of 7\sqrt{5}-7\sqrt{3} by 7 to get \sqrt{5}-\sqrt{3}.

$$\sqrt{5}-\sqrt{3}$$