Evaluate
\sqrt{10}+2\sqrt{7}\approx 8.453780282
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\sqrt{2}\sqrt{14}+\sqrt{2}\sqrt{5}
Use the distributive property to multiply \sqrt{2} by \sqrt{14}+\sqrt{5}.
\sqrt{2}\sqrt{2}\sqrt{7}+\sqrt{2}\sqrt{5}
Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.
2\sqrt{7}+\sqrt{2}\sqrt{5}
Multiply \sqrt{2} and \sqrt{2} to get 2.
2\sqrt{7}+\sqrt{10}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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}