\sqrt { ( \frac { 22,5 } { 2 } ) ^ { 2 } }
Evaluate
11,25
Factor
\frac{5 \cdot 3 ^ {2}}{2 ^ {2}} = 11\frac{1}{4} = 11.25
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\sqrt{\left(\frac{225}{20}\right)^{2}}
Expand \frac{22,5}{2} by multiplying both numerator and the denominator by 10.
\sqrt{\left(\frac{45}{4}\right)^{2}}
Reduce the fraction \frac{225}{20} to lowest terms by extracting and canceling out 5.
\sqrt{\frac{2025}{16}}
Calculate \frac{45}{4} to the power of 2 and get \frac{2025}{16}.
\frac{45}{4}
Rewrite the square root of the division \frac{2025}{16} as the division of square roots \frac{\sqrt{2025}}{\sqrt{16}}. Take the square root of both numerator and denominator.
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}