Solve 19.2+248/19.2*35*sqrt{9.8/0.4}

$$\frac{ 19.2+248 }{ 19.2 } \times 35 \times \sqrt{ \frac{ 9.8 }{ 0.4 } }$$

Evaluate

$$\frac{40915\sqrt{2}}{24}\approx 2410.939496021$$

Solution Steps

Add 19.2 and 248 to get 267.2.

$$35\times \frac{267.2}{19.2}\sqrt{\frac{9.8}{0.4}}$$

Expand \frac{267.2}{19.2} by multiplying both numerator and the denominator by 10.

$$35\times \frac{2672}{192}\sqrt{\frac{9.8}{0.4}}$$

Reduce the fraction \frac{2672}{192} to lowest terms by extracting and canceling out 16.

$$35\times \frac{167}{12}\sqrt{\frac{9.8}{0.4}}$$

Express 35\times \frac{167}{12} as a single fraction.

$$\frac{35\times 167}{12}\sqrt{\frac{9.8}{0.4}}$$

Multiply 35 and 167 to get 5845.

$$\frac{5845}{12}\sqrt{\frac{9.8}{0.4}}$$

Expand \frac{9.8}{0.4} by multiplying both numerator and the denominator by 10.

$$\frac{5845}{12}\sqrt{\frac{98}{4}}$$

Reduce the fraction \frac{98}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5845}{12}\sqrt{\frac{49}{2}}$$

Rewrite the square root of the division \sqrt{\frac{49}{2}} as the division of square roots \frac{\sqrt{49}}{\sqrt{2}}.

$$\frac{5845}{12}\times \frac{\sqrt{49}}{\sqrt{2}}$$

Calculate the square root of 49 and get 7.

$$\frac{5845}{12}\times \frac{7}{\sqrt{2}}$$

Rationalize the denominator of \frac{7}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5845}{12}\times \frac{7\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5845}{12}\times \frac{7\sqrt{2}}{2}$$

Multiply \frac{5845}{12} times \frac{7\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5845\times 7\sqrt{2}}{12\times 2}$$

Multiply 5845 and 7 to get 40915.

$$\frac{40915\sqrt{2}}{12\times 2}$$

Multiply 12 and 2 to get 24.

$$\frac{40915\sqrt{2}}{24}$$