Add/Simplify to identify the like radicals

[LMande]

5sqrt12 + sqrt 75

The first step I have is the factor using the greatest perfect square factors.

5sqrt (6*2) + sqrt 75

Then I take the square root of each factor??

5sqrt 6 * sqrt 2 + sqrt 75

5sqrt 2 + sqrt75


blah blah blah... I'm lost and I'm not sure that I've started this correctly but any help would be greatly appreciated! )

 

[jonboy]

5sqrt12 + sqrt 75

The first step I have is the factor using the greatest perfect square factors.

5sqrt (6*2) + sqrt 75

Then I take the square root of each factor??

5sqrt 6 * sqrt 2 + sqrt 75

5sqrt 2 + sqrt75


blah blah blah... I'm lost and I'm not sure that I've started this correctly but any help would be greatly appreciated! )

Hello LMande!

All I did was just simplify and then add them up.


\(\displaystyle \L 5sqrt{12}\,\to\,5sqrt{4\bullet3}\,\to\,5sqrt{2\bullet2\bullet3}\,\to\,10sqrt{3}\)


\(\displaystyle \L sqrt{75}\,\to\,sqrt{5\bullet15}\,\to\,sqrt{5\bullet5\bullet3}\,\to\,5sqrt{3}\)


.............\(\displaystyle \L \;10sqrt{3}\,+\,5sqrt{3}\,=\,15sqrt{3}\)

You can add the \(\displaystyle 10sqrt{3}\) and \(\displaystyle 5sqrt{3}\) because they both terms have the same radical number but it stays the same except for the actual whole number to the left of the sqrt when adding.

 

[galactus]

\(\displaystyle \L\\5\sqrt{12}+\sqrt{75}\)

\(\displaystyle \L\\5\sqrt{4\cdot{3}}+\sqrt{25\cdot{3}}\)

\(\displaystyle \L\\5\cdot{2}\sqrt{3}+5\sqrt{3}\)

\(\displaystyle \L\\10\sqrt{3}+5\sqrt{3}\)

\(\displaystyle \L\\15\sqrt{3}\)

 

[jonboy]

\(\displaystyle \L\\5\sqrt{12}+\sqrt{75}\)

\(\displaystyle \L\\5\sqrt{4\cdot{3}}+\sqrt{25\cdot{3}}\)

\(\displaystyle \L\\5\cdot{2}\sqrt{3}+5\sqrt{3}\)

\(\displaystyle \L\\10\sqrt{3}+5\sqrt{3}\)

\(\displaystyle \L\\15\sqrt{3}\)

Yeah we both got the same answer!

 

[soroban]

Hello, LMande!

\(\displaystyle 5\sqrt{12}\,+\,\sqrt{75}\)

The first step I have is the factor using the greatest perfect square factors.
Evidently you don't understand "greatest perfect square factor."

\(\displaystyle 5\sqrt{6\cdot2} + \sqrt{75}\)
\(\displaystyle \;\:\,\)↑ ↑
no squares!

For each radical: look for the greatest square factor: 4, 9, 16, 25, . . .

\(\displaystyle \;\;\;\sqrt{12}\:=\:\sqrt{4\cdot3} \:=\:\sqrt{4}\cdot\sqrt{3}\:=\:2\sqrt{3}\)

\(\displaystyle \;\;\;\sqrt{75}\:=\:\sqrt{25\cdot3}\:=\:\sqrt{25}\cdot\sqrt{3}\:=\:4\sqrt{3}\)


So the problem becomes: \(\displaystyle \,5\cdot2\sqrt{3}\,+\,5\sqrt{3}\:=\:10\sqrt{3}\,+\,5\sqrt{3}\:=\:15\sqrt{3}\)