Solve sqrt{5.3(1500-83*9.8)/83}

$$\sqrt { \frac { 5.3 ( 1500 - 83 \times 9.8 ) } { 83 } }$$

Evaluate

$$\frac{\sqrt{30203534}}{830}\approx 6.621414693$$

Solution Steps

Multiply 83 and 9.8 to get 813.4.

$$\sqrt{\frac{5.3\left(1500-813.4\right)}{83}}$$

Subtract 813.4 from 1500 to get 686.6.

$$\sqrt{\frac{5.3\times 686.6}{83}}$$

Multiply 5.3 and 686.6 to get 3638.98.

$$\sqrt{\frac{3638.98}{83}}$$

Expand \frac{3638.98}{83} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{363898}{8300}}$$

Reduce the fraction \frac{363898}{8300} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{181949}{4150}}$$

Rewrite the square root of the division \sqrt{\frac{181949}{4150}} as the division of square roots \frac{\sqrt{181949}}{\sqrt{4150}}.

$$\frac{\sqrt{181949}}{\sqrt{4150}}$$

Factor 4150=5^{2}\times 166. Rewrite the square root of the product \sqrt{5^{2}\times 166} as the product of square roots \sqrt{5^{2}}\sqrt{166}. Take the square root of 5^{2}.

$$\frac{\sqrt{181949}}{5\sqrt{166}}$$

Rationalize the denominator of \frac{\sqrt{181949}}{5\sqrt{166}} by multiplying numerator and denominator by \sqrt{166}.

$$\frac{\sqrt{181949}\sqrt{166}}{5\left(\sqrt{166}\right)^{2}}$$

The square of \sqrt{166} is 166.

$$\frac{\sqrt{181949}\sqrt{166}}{5\times 166}$$

To multiply \sqrt{181949} and \sqrt{166}, multiply the numbers under the square root.

$$\frac{\sqrt{30203534}}{5\times 166}$$

Multiply 5 and 166 to get 830.

$$\frac{\sqrt{30203534}}{830}$$