Solve frac{sqrt{9}}{4}-sqrt{75}+1/3-4sqrt{5}

$$\frac{ \sqrt{ 9 } }{ 4 } - \sqrt{ 75 } + \frac{ 1 }{ 3 } -4 \sqrt{ 5 }$$

Evaluate

$$\frac{13}{12}-4\sqrt{5}-5\sqrt{3}\approx -16.521192615$$

Solution Steps

Calculate the square root of 9 and get 3.

$$\frac{3}{4}-\sqrt{75}+\frac{1}{3}-4\sqrt{5}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{3}{4}-5\sqrt{3}+\frac{1}{3}-4\sqrt{5}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{9}{12}-5\sqrt{3}+\frac{4}{12}-4\sqrt{5}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{12}-5\sqrt{3}-4\sqrt{5}$$

Add 9 and 4 to get 13.

$$\frac{13}{12}-5\sqrt{3}-4\sqrt{5}$$

Factor

$$\frac{13 - 48 \sqrt{5} - 60 \sqrt{3}}{12} = -16.521192614510213$$