Solve 4+5sqrt{5}-4.9/3frac{30-5sqrt{5}}{31}

$$4+5 \sqrt{ 5 } - \frac{ 4.9 }{ 3 } \frac{ 30-5 \sqrt{ 5 } }{ 31 }$$

Evaluate

$$\frac{979\sqrt{5}}{186}+\frac{75}{31}\approx 14.188766398$$

Short Solution Steps

Expand \frac{4.9}{3} by multiplying both numerator and the denominator by 10.

$$4+5\sqrt{5}-\frac{49}{30}\times \frac{30-5\sqrt{5}}{31}$$

Multiply \frac{49}{30} times \frac{30-5\sqrt{5}}{31} by multiplying numerator times numerator and denominator times denominator.

$$4+5\sqrt{5}-\frac{49\left(30-5\sqrt{5}\right)}{30\times 31}$$

Multiply 30 and 31 to get 930.

$$4+5\sqrt{5}-\frac{49\left(30-5\sqrt{5}\right)}{930}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4+5\sqrt{5} times \frac{930}{930}.

$$\frac{930\left(4+5\sqrt{5}\right)}{930}-\frac{49\left(30-5\sqrt{5}\right)}{930}$$

Since \frac{930\left(4+5\sqrt{5}\right)}{930} and \frac{49\left(30-5\sqrt{5}\right)}{930} have the same denominator, subtract them by subtracting their numerators.

$$\frac{930\left(4+5\sqrt{5}\right)-49\left(30-5\sqrt{5}\right)}{930}$$

Do the multiplications in 930\left(4+5\sqrt{5}\right)-49\left(30-5\sqrt{5}\right).

$$\frac{3720+4650\sqrt{5}-1470+245\sqrt{5}}{930}$$

Do the calculations in 3720+4650\sqrt{5}-1470+245\sqrt{5}.

$$\frac{2250+4895\sqrt{5}}{930}$$

Factor

$$\frac{979 \sqrt{5} + 450}{186} = 14.188766397700508$$