Solve 270.625-269.3/0.523/sqrt{8}

$$\frac { 270.625 - 269.3 } { 0.523 / \sqrt { 8 } }$$

Evaluate

$$\frac{2650\sqrt{2}}{523}\approx 7.165709255$$

Solution Steps

Subtract 269.3 from 270.625 to get 1.325.

$$\frac{1.325}{\frac{0.523}{\sqrt{8}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{1.325}{\frac{0.523}{2\sqrt{2}}}$$

Rationalize the denominator of \frac{0.523}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1.325}{\frac{0.523\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{1.325}{\frac{0.523\sqrt{2}}{2\times 2}}$$

Multiply 2 and 2 to get 4.

$$\frac{1.325}{\frac{0.523\sqrt{2}}{4}}$$

Divide 0.523\sqrt{2} by 4 to get 0.13075\sqrt{2}.

$$\frac{1.325}{0.13075\sqrt{2}}$$

Rationalize the denominator of \frac{1.325}{0.13075\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1.325\sqrt{2}}{0.13075\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1.325\sqrt{2}}{0.13075\times 2}$$

Multiply 0.13075 and 2 to get 0.2615.

$$\frac{1.325\sqrt{2}}{0.2615}$$

Divide 1.325\sqrt{2} by 0.2615 to get \frac{2650}{523}\sqrt{2}.

$$\frac{2650}{523}\sqrt{2}$$