Solve (sqrt{75}-sqrt{15})divsqrt{3}=

$$( \sqrt { 75 } - \sqrt { 15 } ) \div \sqrt { 3 } =$$

Evaluate

$$5-\sqrt{5}\approx 2.763932023$$

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}.

$$\frac{5\sqrt{3}-\sqrt{15}}{\sqrt{3}}$$

Rationalize the denominator of \frac{5\sqrt{3}-\sqrt{15}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(5\sqrt{3}-\sqrt{15}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(5\sqrt{3}-\sqrt{15}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 5\sqrt{3}-\sqrt{15} by \sqrt{3}.

$$\frac{5\left(\sqrt{3}\right)^{2}-\sqrt{15}\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{5\times 3-\sqrt{15}\sqrt{3}}{3}$$

Multiply 5 and 3 to get 15.

$$\frac{15-\sqrt{15}\sqrt{3}}{3}$$

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}.

$$\frac{15-\sqrt{3}\sqrt{5}\sqrt{3}}{3}$$

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

$$\frac{15-3\sqrt{5}}{3}$$

Divide each term of 15-3\sqrt{5} by 3 to get 5-\sqrt{5}.

$$5-\sqrt{5}$$