Solve frac{sqrt{5*10^3}}{sqrt{15}}

$$\frac{ \sqrt{ 5 \times { 10 }^{ 3 } } }{ \sqrt{ 15 } }$$

Evaluate

$$\frac{10\sqrt{30}}{3}\approx 18.257418584$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{\sqrt{5\times 1000}}{\sqrt{15}}$$

Multiply 5 and 1000 to get 5000.

$$\frac{\sqrt{5000}}{\sqrt{15}}$$

Factor 5000=50^{2}\times 2. Rewrite the square root of the product \sqrt{50^{2}\times 2} as the product of square roots \sqrt{50^{2}}\sqrt{2}. Take the square root of 50^{2}.

$$\frac{50\sqrt{2}}{\sqrt{15}}$$

Rationalize the denominator of \frac{50\sqrt{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{50\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{50\sqrt{2}\sqrt{15}}{15}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{50\sqrt{30}}{15}$$

Divide 50\sqrt{30} by 15 to get \frac{10}{3}\sqrt{30}.

$$\frac{10}{3}\sqrt{30}$$