Solve 2143*27/sqrt{52}=

$$\frac { 2143 \times 27 } { \sqrt { 52 } } =$$

Evaluate

$$\frac{57861\sqrt{13}}{26}\approx 8023.877013447$$

Solution Steps

Multiply 2143 and 27 to get 57861.

$$\frac{57861}{\sqrt{52}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{57861}{2\sqrt{13}}$$

Rationalize the denominator of \frac{57861}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{57861\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{57861\sqrt{13}}{2\times 13}$$

Multiply 2 and 13 to get 26.

$$\frac{57861\sqrt{13}}{26}$$