To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
The technical storage or access that is used exclusively for statistical purposes.
The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
3 Responses
Square roots are fussy roommates: they won’t share one radical sign under addition (√a + √b ≠ √(a+b))-check by squaring: (√2+√8)^2=18 but (√10)^2=10-while they do cooperate under multiplication, so √12 = √(4·3) = √4·√3 = 2√3, not 3+√3; see more here: https://www.khanacademy.org/math/algebra/rational-exponents-radicals/alg1-radicals/a/simplifying-square-roots. Hope this helps!
I like to check by squaring: (√a + √b)² = a + b + 2√(ab), so addition doesn’t stay inside the root; instead tidy by pulling out perfect squares, e.g., √12 = √(4·3) = 2√3 (not √9 + √3), and √2 + √8 = √2 + 2√2 = 3√2 ≠ √10.
Quick refresher: https://www.khanacademy.org/math/algebra/radical-expressions-and-equations/simplifying-square-roots/v/simplifying-square-roots
Pattern check time: square both sides to test your rule-(sqrt(2)+sqrt(8))^2 = 2+8+2*sqrt(16) = 18, while (sqrt(10))^2 = 10, so sqrt doesn’t distribute over addition; the “tidy” move is to factor inside the root, e.g., sqrt(12) = sqrt(4*3) = 2*sqrt(3) (not 3 + sqrt(3)). I’m pretty sure the only cases where sqrt(a)+sqrt(b)=sqrt(a+b) work are trivial like ab=0 (maybe a=b=1 too?), but otherwise split by factors, not sums.