+26387 How does sqrt(x-3)^2=x-3?
1.
\(\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left(~ \sqrt{x-3} ~ \right)^2 \\ \hline \end{array} \)
2.
\(\begin{array}{|rcll|} \hline \sqrt{x-3} &=& (x-3)^{\frac12} \\ \hline \end{array} \)
3.
\(\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left( ~ \sqrt{x-3} ~ \right)^2 \\ &=& \left( ~ (x-3)^{\frac12} ~ \right)^2 \\ &=& (x-3)^{\frac12\cdot 2} \\ &=& (x-3)^{\frac22 } \\ &=& (x-3)^{1} \\ &=& (x-3) \\ \hline \end{array} \)
+26387 How does sqrt(x-3)^2=x-3?
1.
\(\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left(~ \sqrt{x-3} ~ \right)^2 \\ \hline \end{array} \)
2.
\(\begin{array}{|rcll|} \hline \sqrt{x-3} &=& (x-3)^{\frac12} \\ \hline \end{array} \)
3.
\(\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left( ~ \sqrt{x-3} ~ \right)^2 \\ &=& \left( ~ (x-3)^{\frac12} ~ \right)^2 \\ &=& (x-3)^{\frac12\cdot 2} \\ &=& (x-3)^{\frac22 } \\ &=& (x-3)^{1} \\ &=& (x-3) \\ \hline \end{array} \)
