Evaluate
24\sqrt{7}+74\approx 137.498031466
Expand
24 \sqrt{7} + 74 = 137.498031466
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\left(-4\sqrt{7}-3\right)^{2}-47
Add -11 and 8 to get -3.
16\left(\sqrt{7}\right)^{2}+24\sqrt{7}+9-47
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4\sqrt{7}-3\right)^{2}.
16\times 7+24\sqrt{7}+9-47
The square of \sqrt{7} is 7.
112+24\sqrt{7}+9-47
Multiply 16 and 7 to get 112.
121+24\sqrt{7}-47
Add 112 and 9 to get 121.
74+24\sqrt{7}
Subtract 47 from 121 to get 74.
\left(-4\sqrt{7}-3\right)^{2}-47
Add -11 and 8 to get -3.
16\left(\sqrt{7}\right)^{2}+24\sqrt{7}+9-47
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4\sqrt{7}-3\right)^{2}.
16\times 7+24\sqrt{7}+9-47
The square of \sqrt{7} is 7.
112+24\sqrt{7}+9-47
Multiply 16 and 7 to get 112.
121+24\sqrt{7}-47
Add 112 and 9 to get 121.
74+24\sqrt{7}
Subtract 47 from 121 to get 74.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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}