Search 75,605 tutors
Ask a question
0 0

Why is it important to find nonperfect roots in radical form to simplify the process of performing basic operations with radical expressions?

NEED HELP ASAP!!
Tutors, please sign in to answer this question.

2 Answers

"Why is it important to find nonperfect roots in radical form to simplify the process of performing basic operations with radical expressions?"

A "nonperfect" root must mean the root of a number that is not a perfect square.

Consider E = √(48) + √(175) - √(63). How would you simplify it?

First factorize each radicand into its prime factors:

E = √(2*2*2*3*3) + √(5*5*7) - √(3*3*7)

Every pair of identical primes under a radical represents a perfect square and can be replaced by one of those primes as a factor outside of the radical. Do that until there are no more pairs of primes under the radical and the radical that's left is a "nonperfect root".

E = 2*3*√(2) + 5*√(7) - 3*√(7)

And now you can identify and combine any "like terms":

E = 6√(2) + 2√(7)

So the short answer to the question is, "to identify and combine like terms".
If I understand the question correctly.

We can multiply and divide the radicals , but we can not add or subtract:

ie,  √3 . √2 = √6.

However:

√3 + √2  , can not yield to another radical with a given radicand  such as √5

Can only add radicals of equal radicand, ie.   √7 +2√7 = 3 √7.

So , with this property of radicals, we can simplify the radicals, and if come up with multiple of simple radicals the we add.

√50 + √18 - √8 =

√(2 . 5 . 5 ) + √( 2 . 3 . 3 ) - √ (2 . 2 . 2) =

√(2. 5^2)  +  √(2 .3^2)  -√ (  2 .2^2)  =

√2 . √5^2  + √2 . √3^2  -  √2 . √2^2 =

5 √2  + 3 √2 - 2√2 = 6 √2