Solve 3sqrt{15}divsqrt{3}=3sqrt{5}

$$3 \sqrt { 15 } \div \sqrt { 3 } = 3 \sqrt { 5 }$$

Verify

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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}.

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

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

$$\frac{3\times 3\sqrt{5}}{3}=3\sqrt{5}$$

Cancel out 3 and 3.

$$3\sqrt{5}=3\sqrt{5}$$

Subtract 3\sqrt{5} from both sides.

$$3\sqrt{5}-3\sqrt{5}=0$$

Combine 3\sqrt{5} and -3\sqrt{5} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$