Solve frac{98+(sqrt{(98^2+4*4.8*100)}}{9.8}

$$\frac{ 98+( \sqrt{ ( { 98 }^{ 2 } +4 \times 4.8 \times 100) } }{ 9.8 }$$

Evaluate

$$\frac{10\sqrt{2881}}{49}+98\approx 108.954070939$$

Solution Steps

Calculate 98 to the power of 2 and get 9604.

$$98+\frac{\sqrt{9604+4\times 4.8\times 100}}{9.8}$$

Multiply 4 and 4.8 to get 19.2.

$$98+\frac{\sqrt{9604+19.2\times 100}}{9.8}$$

Multiply 19.2 and 100 to get 1920.

$$98+\frac{\sqrt{9604+1920}}{9.8}$$

Add 9604 and 1920 to get 11524.

$$98+\frac{\sqrt{11524}}{9.8}$$

Factor 11524=2^{2}\times 2881. Rewrite the square root of the product \sqrt{2^{2}\times 2881} as the product of square roots \sqrt{2^{2}}\sqrt{2881}. Take the square root of 2^{2}.

$$98+\frac{2\sqrt{2881}}{9.8}$$

Divide 2\sqrt{2881} by 9.8 to get \frac{10}{49}\sqrt{2881}.

$$98+\frac{10}{49}\sqrt{2881}$$

Factor

$$\frac{2 {(5 \sqrt{2881} + 2401)}}{49} = 108.95407093903644$$