Solve 250*2.7/sqrt{52}

$$\frac{ 250 \cdot 2.7 }{ \sqrt{ 52 } }$$

Evaluate

$$\frac{675\sqrt{13}}{26}\approx 93.605658113$$

Solution Steps

Multiply 250 and 2.7 to get 675.

$$\frac{675}{\sqrt{52}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{675}{2\sqrt{13}}$$

Rationalize the denominator of \frac{675}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{675\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{675\sqrt{13}}{2\times 13}$$

Multiply 2 and 13 to get 26.

$$\frac{675\sqrt{13}}{26}$$