Evaluate
33-20\sqrt{2}\approx 4.715728753
Expand
33-20\sqrt{2}
Share
Copied to clipboard
4\left(\sqrt{2}\right)^{2}-20\sqrt{2}+25
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{2}-5\right)^{2}.
4\times 2-20\sqrt{2}+25
The square of \sqrt{2} is 2.
8-20\sqrt{2}+25
Multiply 4 and 2 to get 8.
33-20\sqrt{2}
Add 8 and 25 to get 33.
4\left(\sqrt{2}\right)^{2}-20\sqrt{2}+25
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{2}-5\right)^{2}.
4\times 2-20\sqrt{2}+25
The square of \sqrt{2} is 2.
8-20\sqrt{2}+25
Multiply 4 and 2 to get 8.
33-20\sqrt{2}
Add 8 and 25 to get 33.
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}