Solve 333.3*2/sqrt{76}

$$\frac{ 333.3 \cdot 2 }{ \sqrt{ 76 } }$$

Evaluate

$$\frac{3333\sqrt{19}}{190}\approx 76.464264099$$

Solution Steps

Multiply 333.3 and 2 to get 666.6.

$$\frac{666.6}{\sqrt{76}}$$

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}.

$$\frac{666.6}{2\sqrt{19}}$$

Rationalize the denominator of \frac{666.6}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{666.6\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{666.6\sqrt{19}}{2\times 19}$$

Multiply 2 and 19 to get 38.

$$\frac{666.6\sqrt{19}}{38}$$

Divide 666.6\sqrt{19} by 38 to get \frac{3333}{190}\sqrt{19}.

$$\frac{3333}{190}\sqrt{19}$$