Solve sqrt{(0.18)^2+(0.24)^2/0.38499}

$$\sqrt { \frac { ( 0.18 ) ^ { 2 } + ( 0.24 ) ^ { 2 } } { 0.38499 } }$$

Evaluate

$$\frac{10\sqrt{384990}}{12833}\approx 0.483500058$$

Solution Steps

Calculate 0.18 to the power of 2 and get 0.0324.

$$\sqrt{\frac{0.0324+0.24^{2}}{0.38499}}$$

Calculate 0.24 to the power of 2 and get 0.0576.

$$\sqrt{\frac{0.0324+0.0576}{0.38499}}$$

Add 0.0324 and 0.0576 to get 0.09.

$$\sqrt{\frac{0.09}{0.38499}}$$

Expand \frac{0.09}{0.38499} by multiplying both numerator and the denominator by 100000.

$$\sqrt{\frac{9000}{38499}}$$

Reduce the fraction \frac{9000}{38499} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{3000}{12833}}$$

Rewrite the square root of the division \sqrt{\frac{3000}{12833}} as the division of square roots \frac{\sqrt{3000}}{\sqrt{12833}}.

$$\frac{\sqrt{3000}}{\sqrt{12833}}$$

Factor 3000=10^{2}\times 30. Rewrite the square root of the product \sqrt{10^{2}\times 30} as the product of square roots \sqrt{10^{2}}\sqrt{30}. Take the square root of 10^{2}.

$$\frac{10\sqrt{30}}{\sqrt{12833}}$$

Rationalize the denominator of \frac{10\sqrt{30}}{\sqrt{12833}} by multiplying numerator and denominator by \sqrt{12833}.

$$\frac{10\sqrt{30}\sqrt{12833}}{\left(\sqrt{12833}\right)^{2}}$$

The square of \sqrt{12833} is 12833.

$$\frac{10\sqrt{30}\sqrt{12833}}{12833}$$

To multiply \sqrt{30} and \sqrt{12833}, multiply the numbers under the square root.

$$\frac{10\sqrt{384990}}{12833}$$