Solve sqrt{7500}-(55-5sqrt{3}1)div2

$$\sqrt{ 7500 } -(55-5 \sqrt{ 3 } 1) \div 2$$

Evaluate

$$\frac{105\sqrt{3}-55}{2}\approx 63.432667397$$

Short Solution Steps

Factor 7500=50^{2}\times 3. Rewrite the square root of the product \sqrt{50^{2}\times 3} as the product of square roots \sqrt{50^{2}}\sqrt{3}. Take the square root of 50^{2}.

$$50\sqrt{3}-\frac{55-1\times 5\sqrt{3}}{2}$$

Multiply 1 and 5 to get 5.

$$50\sqrt{3}-\frac{55-5\sqrt{3}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 50\sqrt{3} times \frac{2}{2}.

$$\frac{2\times 50\sqrt{3}}{2}-\frac{55-5\sqrt{3}}{2}$$

Since \frac{2\times 50\sqrt{3}}{2} and \frac{55-5\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 50\sqrt{3}-\left(55-5\sqrt{3}\right)}{2}$$

Do the multiplications in 2\times 50\sqrt{3}-\left(55-5\sqrt{3}\right).

$$\frac{100\sqrt{3}-55+5\sqrt{3}}{2}$$

Do the calculations in 100\sqrt{3}-55+5\sqrt{3}.

$$\frac{105\sqrt{3}-55}{2}$$

Factor

$$\frac{5 {(21 \sqrt{3} - 11)}}{2} = 63.43266739736606$$