Question

I have to add/subtract these expressions, but first I must simplify all of the radicals to determine if they can be combined. Here's my question: 7(Times the square root of 2) - 3(Times the square root of 2) + 4(Times the square root of 5). The last part of the expression is tripping me up! Can someone please help?

Answer 1

i would try the equation editor below, might help a bit

Answer 2

\[7\sqrt{2}-3\sqrt{2}+4\sqrt{5}\]

Answer 3

\(7\sqrt{2}-3\sqrt{2}+4\sqrt{5}=4\sqrt{2}+4\sqrt{5}=4(\sqrt{2}+\sqrt{5})\)

Answer 4

leave \(\sqrt5\) term alone
it is like
\[7x-3x+4y\]

Answer 5

@zzr0ck3r, How do you get that, though? I appreciate the help!

Answer 6

can you combine like terms here
\[7x-3x+4y\]?

Answer 7

@satellite73, I'm not sure if we're using variables for this.

Answer 8

because it illustrates that just as \(7x\) and \(-3x\) are like terms, and therefore \(7x-3x=4x\) that
\[7\sqrt2-3\sqrt2=4\sqrt2\]

Answer 9

but \(4y\) is not a like term, so you cannot combine it
and similarly \(4\sqrt5\) is not a like term with \(4\sqrt2\)

Answer 10

Here's the question I answered and got right prior to this one: \[2\sqrt{5}+4\sqrt{5}-\sqrt{5}=5\sqrt{5}\] I think of them as like fractions with common denominators... Is that the right idea? And I just add/subtract the multipliers before the square roots. Ah! I'm so discombobulated!

Answer 11

Oh, I get it! @satellite73 Thank you! So is that my answer? Do I just combine the like terms and leave out the \[4\sqrt{5}\]?