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

1 Answer
Jul 3, 2016

Answer:

#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#