When can two square roots or radicals be added/subtracted? Create an example of your own to explain your answer.

Mathematics

1 answer:

Gnom [1K]3 years ago

6 0

Tbh i believe you have to subtracted it

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Answer:

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Step-by-step explanation:

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Find the length of a line segment ---

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$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&C&(~ -3 &,& 1~) 
% (c,d)
&D&(~ 5 &,& 6~)
\end{array}~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
CD=\sqrt{[5-(-3)]^2+[6-1]^2}\implies CD=\sqrt{(5+3)^2+(6-1)^2}
\\\\\\
CD=\sqrt{8^2+5^2}\implies CD=\sqrt{64+25}\implies CD=\sqrt{89}$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&F&(~ -6 &,& 4~) 
% (c,d)
&G&(~ 8 &,& -2~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{8-6}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{2}{2} \right)\implies (1,1)$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~) 
% (c,d)
&&(~ 1 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{1-(-2)}\implies \cfrac{1+3}{1+2}\implies \cfrac{4}{3}$

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