Solve 1/2tan(15)sqrt{20}-1

$$\frac{ 1 }{ 2 \tan ( 15 ) } \sqrt{ 20 } -1$$

Evaluate

$$\frac{10000000000000000\sqrt{5}}{2679491924311227}-1\approx 7.345119301$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{2 \cdot 0.2679491924311227} \sqrt{20} - 1$$

Multiply 2 and 0.2679491924311227 to get 0.5358983848622454.

$$\frac{1}{0.5358983848622454}\sqrt{20}-1$$

Expand \frac{1}{0.5358983848622454} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{10000000000000000}{5358983848622454}\sqrt{20}-1$$

Reduce the fraction \frac{10000000000000000}{5358983848622454} to lowest terms by extracting and canceling out 2.

$$\frac{5000000000000000}{2679491924311227}\sqrt{20}-1$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{5000000000000000}{2679491924311227}\times 2\sqrt{5}-1$$

Express \frac{5000000000000000}{2679491924311227}\times 2 as a single fraction.

$$\frac{5000000000000000\times 2}{2679491924311227}\sqrt{5}-1$$

Multiply 5000000000000000 and 2 to get 10000000000000000.

$$\frac{10000000000000000}{2679491924311227}\sqrt{5}-1$$

Factor

$$\frac{10000000000000000 \sqrt{5}}{2679491924311227} - 1 = 7.345119301$$