Solve 500*27/sqrt{76}=

$$\frac { 500 \times 27 } { \sqrt { 76 } } =$$

Evaluate

$$\frac{6750\sqrt{19}}{19}\approx 1548.556203626$$

Solution Steps

Multiply 500 and 27 to get 13500.

$$\frac{13500}{\sqrt{76}}$$

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$\frac{13500}{2\sqrt{19}}$$

Rationalize the denominator of \frac{13500}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{13500\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{13500\sqrt{19}}{2\times 19}$$

Cancel out 2 in both numerator and denominator.

$$\frac{6750\sqrt{19}}{19}$$