Evaluate
\frac{7\left(\sqrt{5}+7\right)}{44}\approx 1.469374451
Share
Copied to clipboard
\frac{7\left(7+\sqrt{5}\right)}{\left(7-\sqrt{5}\right)\left(7+\sqrt{5}\right)}
Rationalize the denominator of \frac{7}{7-\sqrt{5}} by multiplying numerator and denominator by 7+\sqrt{5}.
\frac{7\left(7+\sqrt{5}\right)}{7^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(7-\sqrt{5}\right)\left(7+\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{7\left(7+\sqrt{5}\right)}{49-5}
Square 7. Square \sqrt{5}.
\frac{7\left(7+\sqrt{5}\right)}{44}
Subtract 5 from 49 to get 44.
\frac{49+7\sqrt{5}}{44}
Use the distributive property to multiply 7 by 7+\sqrt{5}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}