Solve sqrt{2*1500*140000/220+7500*7500}

$$\sqrt{ \frac{ 2 \times 1500 \times 140000 }{ 220 } +7500 \times 7500 }$$

Evaluate

$$\frac{500\sqrt{28149}}{11}\approx 7626.210783154$$

Solution Steps

Multiply 2 and 1500 to get 3000.

$$\sqrt{\frac{3000\times 140000}{220}+7500\times 7500}$$

Multiply 3000 and 140000 to get 420000000.

$$\sqrt{\frac{420000000}{220}+7500\times 7500}$$

Reduce the fraction \frac{420000000}{220} to lowest terms by extracting and canceling out 20.

$$\sqrt{\frac{21000000}{11}+7500\times 7500}$$

Multiply 7500 and 7500 to get 56250000.

$$\sqrt{\frac{21000000}{11}[phone]}$$

Convert 56250000 to fraction \frac{618750000}{11}.

$$\sqrt{\frac{21000000}{11}+\frac{618750000}{11}}$$

Since \frac{21000000}{11} and \frac{618750000}{11} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{21000000+618750000}{11}}$$

Add 21000000 and 618750000 to get 639750000.

$$\sqrt{\frac{639750000}{11}}$$

Rewrite the square root of the division \sqrt{\frac{639750000}{11}} as the division of square roots \frac{\sqrt{639750000}}{\sqrt{11}}.

$$\frac{\sqrt{639750000}}{\sqrt{11}}$$

Factor 639750000=500^{2}\times 2559. Rewrite the square root of the product \sqrt{500^{2}\times 2559} as the product of square roots \sqrt{500^{2}}\sqrt{2559}. Take the square root of 500^{2}.

$$\frac{500\sqrt{2559}}{\sqrt{11}}$$

Rationalize the denominator of \frac{500\sqrt{2559}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{500\sqrt{2559}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{500\sqrt{2559}\sqrt{11}}{11}$$

To multiply \sqrt{2559} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{500\sqrt{28149}}{11}$$