Evaluate
500\sqrt{3}+1625\approx 2491.025403784
Expand
500 \sqrt{3} + 1625 = 2491.025403784
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100\left(\sqrt{15}\right)^{2}+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10\sqrt{15}+5\sqrt{5}\right)^{2}.
100\times 15+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
The square of \sqrt{15} is 15.
1500+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Multiply 100 and 15 to get 1500.
1500+100\sqrt{5}\sqrt{3}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
1500+100\times 5\sqrt{3}+25\left(\sqrt{5}\right)^{2}
Multiply \sqrt{5} and \sqrt{5} to get 5.
1500+500\sqrt{3}+25\left(\sqrt{5}\right)^{2}
Multiply 100 and 5 to get 500.
1500+500\sqrt{3}+25\times 5
The square of \sqrt{5} is 5.
1500+500\sqrt{3}+125
Multiply 25 and 5 to get 125.
1625+500\sqrt{3}
Add 1500 and 125 to get 1625.
100\left(\sqrt{15}\right)^{2}+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10\sqrt{15}+5\sqrt{5}\right)^{2}.
100\times 15+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
The square of \sqrt{15} is 15.
1500+100\sqrt{15}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Multiply 100 and 15 to get 1500.
1500+100\sqrt{5}\sqrt{3}\sqrt{5}+25\left(\sqrt{5}\right)^{2}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
1500+100\times 5\sqrt{3}+25\left(\sqrt{5}\right)^{2}
Multiply \sqrt{5} and \sqrt{5} to get 5.
1500+500\sqrt{3}+25\left(\sqrt{5}\right)^{2}
Multiply 100 and 5 to get 500.
1500+500\sqrt{3}+25\times 5
The square of \sqrt{5} is 5.
1500+500\sqrt{3}+125
Multiply 25 and 5 to get 125.
1625+500\sqrt{3}
Add 1500 and 125 to get 1625.
Examples
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Matrix
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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}