Solve 1.253*0.41/sqrt{8*7}=

$$1.253 \times \frac { 0.41 } { \sqrt { 8 \times 7 } } =$$

Evaluate

$$\frac{7339\sqrt{14}}{400000}\approx 0.068650059$$

Solution Steps

Multiply 8 and 7 to get 56.

$$1.253\times \frac{0.41}{\sqrt{56}}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$1.253\times \frac{0.41}{2\sqrt{14}}$$

Rationalize the denominator of \frac{0.41}{2\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$1.253\times \frac{0.41\sqrt{14}}{2\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$1.253\times \frac{0.41\sqrt{14}}{2\times 14}$$

Multiply 2 and 14 to get 28.

$$1.253\times \frac{0.41\sqrt{14}}{28}$$

Divide 0.41\sqrt{14} by 28 to get \frac{41}{2800}\sqrt{14}.

$$1.253\times \frac{41}{2800}\sqrt{14}$$

Multiply 1.253 and \frac{41}{2800} to get 0.0183475.

$$0.0183475\sqrt{14}$$