Solve =4sqrt{3}divsqrt{15}

$$= 4 \sqrt { 3 } \div \sqrt { 15 }$$

Evaluate

$$\frac{4\sqrt{5}}{5}\approx 1.788854382$$

Solution Steps

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{4\sqrt{3}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{4\sqrt{3}\sqrt{15}}{15}$$

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}.

$$\frac{4\sqrt{3}\sqrt{3}\sqrt{5}}{15}$$

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

$$\frac{4\times 3\sqrt{5}}{15}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{5}}{15}$$

Divide 12\sqrt{5} by 15 to get \frac{4}{5}\sqrt{5}.

$$\frac{4}{5}\sqrt{5}$$