How do you subtract 33√2−73√128?

2 Answers
Dillin N.
Dec 8, 2017

−253√2

Explanation:

Remember, that to add and subtract radicals you need to have the same radicals on both sides ex: √2−5√2=−4√2

Now to make them the same radicals we need to simplify 73√128 by breaking down 128 in to it's prime factorization.

128=2⋅64=2⋅2⋅32=2⋅2⋅2⋅16=2⋅2⋅2⋅2⋅8=2⋅2⋅2⋅2⋅2⋅4=2⋅2⋅2⋅2⋅2⋅2⋅2

Next, we can rewrite 73√128 with it's prime factorizations

73√128=73√23⋅23⋅2=2⋅2⋅73√2=283√2

Finally, we can now subtract the two radicals

33√2−283√2=−253√2

MeneerNask
Dec 8, 2017

With radicals it helps if you can take powers from under the root sign.

Explanation:

Since these are third roots, we have to take out third powers:

128=27=2×26=2×(22)3

So we can take out 22=4 and leave the other 2 under the root:

So: 3√128=43√2

The original problem then turns into:

=33√2−(7×4)3√2

And since the radicals are all the same, we can subtract:

=(3−28)×3√2=−213√2

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