Solve 214.3*2.7/sqrt{76}

$$\frac{ 214.3 \cdot 2.7 }{ \sqrt{ 76 } }$$

Evaluate

$$\frac{57861\sqrt{19}}{3800}\approx 66.371118887$$

Solution Steps

Multiply 214.3 and 2.7 to get 578.61.

$$\frac{578.61}{\sqrt{76}}$$

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}.

$$\frac{578.61}{2\sqrt{19}}$$

Rationalize the denominator of \frac{578.61}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{578.61\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{578.61\sqrt{19}}{2\times 19}$$

Multiply 2 and 19 to get 38.

$$\frac{578.61\sqrt{19}}{38}$$

Divide 578.61\sqrt{19} by 38 to get \frac{57861}{3800}\sqrt{19}.

$$\frac{57861}{3800}\sqrt{19}$$