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Adding Unlike Radicals

Q: What if I have to add radicals, but the radicals are different? I am trying to add sqrt{5}+4sqrt{3}.

A: You can’t add those, or simplify any further without a calculator. You just have to leave it as it is, because the square roots are different (3 and 5).

sqrt{5}+4sqrt{3}
=sqrt{5}+4sqrt{3}

Let’s look at some more examples like this:

2sqrt{5}+4sqrt{3}+sqrt{5}+3sqrt{3}
=(2+1)sqrt{5}+(4+3)sqrt{3}
=3sqrt{5}+7sqrt{3}

This is very similar to collecting like terms in algebra:

2x+4y+x+3y
=(2+1)x+(4+3)y
=3x+7y