Solve =sqrt{1.01*10^5*1.4/1.293}

$$= \sqrt { \frac { 1.01 \times 10 ^ { 5 } \times 1.4 } { 1.293 } }$$

Evaluate

$$\frac{200\sqrt{4570755}}{1293}\approx 330.693335252$$

Solution Steps

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{1.01\times 100000\times 1.4}{1.293}}$$

Multiply 1.01 and 100000 to get 101000.

$$\sqrt{\frac{101000\times 1.4}{1.293}}$$

Multiply 101000 and 1.4 to get 141400.

$$\sqrt{\frac{141400}{1.293}}$$

Expand \frac{141400}{1.293} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{141400000}{1293}}$$

Rewrite the square root of the division \sqrt{\frac{141400000}{1293}} as the division of square roots \frac{\sqrt{141400000}}{\sqrt{1293}}.

$$\frac{\sqrt{141400000}}{\sqrt{1293}}$$

Factor 141400000=200^{2}\times 3535. Rewrite the square root of the product \sqrt{200^{2}\times 3535} as the product of square roots \sqrt{200^{2}}\sqrt{3535}. Take the square root of 200^{2}.

$$\frac{200\sqrt{3535}}{\sqrt{1293}}$$

Rationalize the denominator of \frac{200\sqrt{3535}}{\sqrt{1293}} by multiplying numerator and denominator by \sqrt{1293}.

$$\frac{200\sqrt{3535}\sqrt{1293}}{\left(\sqrt{1293}\right)^{2}}$$

The square of \sqrt{1293} is 1293.

$$\frac{200\sqrt{3535}\sqrt{1293}}{1293}$$

To multiply \sqrt{3535} and \sqrt{1293}, multiply the numbers under the square root.

$$\frac{200\sqrt{4570755}}{1293}$$