Solve sqrt{30*3400*1.1111/270^2+300^2}

$$\sqrt{ \frac{ 30 \cdot 3400 \times 1.1111 }{ { 270 }^{ 2 } + { 300 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{512828205}}{27150}\approx 0.834096152$$

Solution Steps

Multiply 30 and 3400 to get 102000.

$$\sqrt{\frac{102000\times 1.1111}{270^{2}+300^{2}}}$$

Multiply 102000 and 1.1111 to get 113332.2.

$$\sqrt{\frac{113332.2}{270^{2}+300^{2}}}$$

Calculate 270 to the power of 2 and get 72900.

$$\sqrt{\frac{113332.2}{72900+300^{2}}}$$

Calculate 300 to the power of 2 and get 90000.

$$\sqrt{\frac{113332.2}{72900+90000}}$$

Add 72900 and 90000 to get 162900.

$$\sqrt{\frac{113332.2}{162900}}$$

Expand \frac{113332.2}{162900} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1133322}{1629000}}$$

Reduce the fraction \frac{1133322}{1629000} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{188887}{271500}}$$

Rewrite the square root of the division \sqrt{\frac{188887}{271500}} as the division of square roots \frac{\sqrt{188887}}{\sqrt{271500}}.

$$\frac{\sqrt{188887}}{\sqrt{271500}}$$

Factor 271500=10^{2}\times 2715. Rewrite the square root of the product \sqrt{10^{2}\times 2715} as the product of square roots \sqrt{10^{2}}\sqrt{2715}. Take the square root of 10^{2}.

$$\frac{\sqrt{188887}}{10\sqrt{2715}}$$

Rationalize the denominator of \frac{\sqrt{188887}}{10\sqrt{2715}} by multiplying numerator and denominator by \sqrt{2715}.

$$\frac{\sqrt{188887}\sqrt{2715}}{10\left(\sqrt{2715}\right)^{2}}$$

The square of \sqrt{2715} is 2715.

$$\frac{\sqrt{188887}\sqrt{2715}}{10\times 2715}$$

To multiply \sqrt{188887} and \sqrt{2715}, multiply the numbers under the square root.

$$\frac{\sqrt{512828205}}{10\times 2715}$$

Multiply 10 and 2715 to get 27150.

$$\frac{\sqrt{512828205}}{27150}$$