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\sqrt{7^{2}-\left(3\sqrt{5}\right)^{2}}
Consider \left(7+3\sqrt{5}\right)\left(7-3\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\sqrt{49-\left(3\sqrt{5}\right)^{2}}
Calculate 7 to the power of 2 and get 49.
\sqrt{49-3^{2}\left(\sqrt{5}\right)^{2}}
Expand \left(3\sqrt{5}\right)^{2}.
\sqrt{49-9\left(\sqrt{5}\right)^{2}}
Calculate 3 to the power of 2 and get 9.
\sqrt{49-9\times 5}
The square of \sqrt{5} is 5.
\sqrt{49-45}
Multiply 9 and 5 to get 45.
\sqrt{4}
Subtract 45 from 49 to get 4.
2
Calculate the square root of 4 and get 2.
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}