Solve 2143*27/sqrt{76}

$$\frac{ 2143 \cdot 27 }{ \sqrt{ 76 } }$$

Evaluate

$$\frac{57861\sqrt{19}}{38}\approx 6637.111888742$$

Solution Steps

Multiply 2143 and 27 to get 57861.

$$\frac{57861}{\sqrt{76}}$$

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}.

$$\frac{57861}{2\sqrt{19}}$$

Rationalize the denominator of \frac{57861}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{57861\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{57861\sqrt{19}}{2\times 19}$$

Multiply 2 and 19 to get 38.

$$\frac{57861\sqrt{19}}{38}$$