Guest wrote:Why does [tex]\sqrt{180}[/tex] = 6[tex]\sqrt{5}[/tex]

[tex]180= 9(2)(10)= 9(2)(2)(2)(5)= (3^2)(2^2)(5)[/tex] so [tex]\sqrt{180}= \sqrt{3^2}\sqrt{2^2}\sqrt{5}= 3(2)\sqrt{5}= 6\sqrt{5}[/tex]

But [tex]\sqrt{48}[/tex] = 4[tex]\sqrt{3}[/tex][/tex]I'm not sure why you say "but". The two are not really related. [tex]48= 16(3)[/tex] so [tex]\sqrt{48}= \sqrt{16}\sqrt{3}= 4\sqrt{3}[/tex].

They are unrelated, but the way I remember doing these is sort of confusing me. This is how I've been asked to do it:

For example:

Why does [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] x [tex]\sqrt{3}[/tex] x [tex]\sqrt{3}[/tex] become 2 x 3 x [tex]\sqrt{5}[/tex]

??? It DOESN'T! [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] x [tex]\sqrt{3}[/tex] x [tex]\sqrt{3}[/tex]= 2(3)= 6. Did you drop a "[tex]\sqrt{5}[/tex]" from the left side?

But then [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex] x [tex]\sqrt{3}[/tex] become 4[tex]\sqrt{3}[/tex] ?

[tex]\sqrt{2}\sqrt{2}= 2[/tex] (by the

definition of "[tex]\sqrt{}[/tex])

wwAm I making sense?

Yes, but you seem to be forgetting that the square root is the "inverse" of squaring: [tex]\sqrt{x^2}= |x|[/tex] (so [tex]\sqrt{x^2]= x[/tex] as long as x is positive and [tex]\left(\sqrt{x}\right)^2= x[/tex].