Sandra was simplifying 45√×23√, and she ended up with 815−−√ as her simplified answer. Is Sandra correct? If she is not correct, what was her mistake?

Answer 1

To simplify the expression $45\sqrt{23}\cdot{}\sqrt{815}$, we first recognize that we can combine the square roots as follows: \begin{align*}
45\sqrt{23}\cdot{}\sqrt{815}&=45\sqrt{23\cdot815}\\
&=45\sqrt{18745}.
\end{align*} Instead of going further, we can conclude that Sandra made a mistake because the expression $\sqrt{815}-\sqrt{18745}$ cannot be simplified any further. Therefore, Sandra's answer is incorrect.