Question

$$SimpI+\sqrt{50,000}-25\sqrt{125+\sqrt{845}$$

Answer

Si*m*pI+5*sqrt(2),-112*sqrt(5)

Solution


Simplify  \(\sqrt{50}\)  to  \(5\sqrt{2}\).
\[SimpI+5\sqrt{2},000-25\sqrt{125}+\sqrt{845}\]
Simplify  \(\sqrt{125}\)  to  \(5\sqrt{5}\).
\[SimpI+5\sqrt{2},000-25\times 5\sqrt{5}+\sqrt{845}\]
Simplify  \(\sqrt{845}\)  to  \(13\sqrt{5}\).
\[SimpI+5\sqrt{2},000-25\times 5\sqrt{5}+13\sqrt{5}\]
Simplify  \(25\times 5\sqrt{5}\)  to  \(125\sqrt{5}\).
\[SimpI+5\sqrt{2},000-125\sqrt{5}+13\sqrt{5}\]
Collect like terms.
\[SimpI+5\sqrt{2},(-125\sqrt{5}+13\sqrt{5})\]
Remove parentheses.
\[SimpI+5\sqrt{2},-125\sqrt{5}+13\sqrt{5}\]
Simplify  \(-125\sqrt{5}+13\sqrt{5}\)  to  \(-112\sqrt{5}\).
\[SimpI+5\sqrt{2},-112\sqrt{5}\]