Solve sqrt{left(9.8*1500-0.6*9.8*1500right)35/1500}

$$\sqrt{ \frac{ \left( 9.8 \cdot 1500-0.6 \cdot 9.8 \cdot 1500 \right) 35 }{ 1500 } }$$

Evaluate

$$\frac{7\sqrt{70}}{5}\approx 11.713240371$$

Solution Steps

Multiply 9.8 and 1500 to get 14700.

$$\sqrt{\frac{\left(14700-0.6\times 9.8\times 1500\right)\times 35}{1500}}$$

Multiply 0.6 and 9.8 to get 5.88.

$$\sqrt{\frac{\left(14700-5.88\times 1500\right)\times 35}{1500}}$$

Multiply 5.88 and 1500 to get 8820.

$$\sqrt{\frac{\left(14700-8820\right)\times 35}{1500}}$$

Subtract 8820 from 14700 to get 5880.

$$\sqrt{\frac{5880\times 35}{1500}}$$

Multiply 5880 and 35 to get 205800.

$$\sqrt{\frac{205800}{1500}}$$

Reduce the fraction \frac{205800}{1500} to lowest terms by extracting and canceling out 300.

$$\sqrt{\frac{686}{5}}$$

Rewrite the square root of the division \sqrt{\frac{686}{5}} as the division of square roots \frac{\sqrt{686}}{\sqrt{5}}.

$$\frac{\sqrt{686}}{\sqrt{5}}$$

Factor 686=7^{2}\times 14. Rewrite the square root of the product \sqrt{7^{2}\times 14} as the product of square roots \sqrt{7^{2}}\sqrt{14}. Take the square root of 7^{2}.

$$\frac{7\sqrt{14}}{\sqrt{5}}$$

Rationalize the denominator of \frac{7\sqrt{14}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{7\sqrt{14}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{7\sqrt{14}\sqrt{5}}{5}$$

To multiply \sqrt{14} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{7\sqrt{70}}{5}$$