Evaluate
23-4\sqrt{15}\approx 7.508066615
Expand
23-4\sqrt{15}
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\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-2\sqrt{5}\right)^{2}.
3-4\sqrt{3}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
The square of \sqrt{3} is 3.
3-4\sqrt{15}+4\left(\sqrt{5}\right)^{2}
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
3-4\sqrt{15}+4\times 5
The square of \sqrt{5} is 5.
3-4\sqrt{15}+20
Multiply 4 and 5 to get 20.
23-4\sqrt{15}
Add 3 and 20 to get 23.
\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-2\sqrt{5}\right)^{2}.
3-4\sqrt{3}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
The square of \sqrt{3} is 3.
3-4\sqrt{15}+4\left(\sqrt{5}\right)^{2}
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
3-4\sqrt{15}+4\times 5
The square of \sqrt{5} is 5.
3-4\sqrt{15}+20
Multiply 4 and 5 to get 20.
23-4\sqrt{15}
Add 3 and 20 to get 23.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}