Evaluate
\sqrt{2}-1\approx 0.414213562
Expand
\sqrt{2} - 1 = 0.414213562
Quiz
Arithmetic
5 problems similar to:
\frac { 1 } { 2 } - \frac { 1 } { 2 } ( \sqrt { 2 } - 1 ) ^ { 2 }
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\frac{1}{2}-\frac{1}{2}\left(\left(\sqrt{2}\right)^{2}-2\sqrt{2}+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-1\right)^{2}.
\frac{1}{2}-\frac{1}{2}\left(2-2\sqrt{2}+1\right)
The square of \sqrt{2} is 2.
\frac{1}{2}-\frac{1}{2}\left(3-2\sqrt{2}\right)
Add 2 and 1 to get 3.
\frac{1}{2}-\frac{3}{2}+\sqrt{2}
Use the distributive property to multiply -\frac{1}{2} by 3-2\sqrt{2}.
-1+\sqrt{2}
Subtract \frac{3}{2} from \frac{1}{2} to get -1.
\frac{1}{2}-\frac{1}{2}\left(\left(\sqrt{2}\right)^{2}-2\sqrt{2}+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-1\right)^{2}.
\frac{1}{2}-\frac{1}{2}\left(2-2\sqrt{2}+1\right)
The square of \sqrt{2} is 2.
\frac{1}{2}-\frac{1}{2}\left(3-2\sqrt{2}\right)
Add 2 and 1 to get 3.
\frac{1}{2}-\frac{3}{2}+\sqrt{2}
Use the distributive property to multiply -\frac{1}{2} by 3-2\sqrt{2}.
-1+\sqrt{2}
Subtract \frac{3}{2} from \frac{1}{2} to get -1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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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}