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\left(\sqrt{3}\right)^{2}-1-\sqrt{16}+\left(\frac{1}{2}\right)^{-1}
Consider \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
3-1-\sqrt{16}+\left(\frac{1}{2}\right)^{-1}
The square of \sqrt{3} is 3.
2-\sqrt{16}+\left(\frac{1}{2}\right)^{-1}
Subtract 1 from 3 to get 2.
2-4+\left(\frac{1}{2}\right)^{-1}
Calculate the square root of 16 and get 4.
-2+\left(\frac{1}{2}\right)^{-1}
Subtract 4 from 2 to get -2.
-2+2
Calculate \frac{1}{2} to the power of -1 and get 2.
0
Add -2 and 2 to get 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}