Question

How do you simplify `7sqrt2 - sqrt32 + sqrt128`?

Answer 1

`11sqrt2`

Explanation:

Write the numbers under the roots as the product of their prime factors:

`7sqrt2 - sqrt (2^5) + sqrt(2^7)`

Make even indices wherever possible, to be able to find the square roots

`7sqrt2 - sqrt (2 xx 2^4) + sqrt(2 xx 2^6)`

=`7sqrt2 - 2^2sqrt 2 + 2^3sqrt2" = " 7sqrt2 - 4sqrt 2 + 8sqrt2`

Now add the like terms: `11sqrt2`