Solve 600*2.7/sqrt{76}

$$\frac{ 600 \cdot 2.7 }{ \sqrt{ 76 } }$$

Evaluate

$$\frac{810\sqrt{19}}{19}\approx 185.826744435$$

Solution Steps

Multiply 600 and 2.7 to get 1620.

$$\frac{1620}{\sqrt{76}}$$

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}.

$$\frac{1620}{2\sqrt{19}}$$

Rationalize the denominator of \frac{1620}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{1620\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{1620\sqrt{19}}{2\times 19}$$

Cancel out 2 in both numerator and denominator.

$$\frac{810\sqrt{19}}{19}$$