Simplifying Radical Expressions, 10 pts for best answer!?

Question

Why is it important to simplify radical expressions before adding

or subtracting? How is adding radical expressions similar to adding polynomial expressions? How

is it different? Provide a radical expression for your classmates to simplify.

Answer 1

16^1/2 + 75^1/2 + 32^1/2 + 225^1/2

= 4 + 5(3)^1/2  + 4(2)^1/2  + 15

= 19 + 5(3)^1/2  + 4(2)^1/2

is an example

it is important as in this case:

44^1/2 + 99^1/2 - 11^1/2

=(4^1/2)(11^1/2)  +(9^1/2)(11^1/2) - (11^1/2)

= 2(11^1/2) +3(11^1/2) - (11^1/2)

=4(11^1/2)

it is similar to adding polynomial expressions like in this case

3^1/2 + 4^1/2 + 5^1/2 +12^1/2 +20^1/2

=3^1/2 + 2 + 5^1/2 + (3^1/2)(4^1/2)  +(4^1/2)(5^1/2)

= 3^1/2 + 2 + 5^1/2 + 2(3^1/2) + 2(5^1/2)

=3(3^1/2) + 3(5^1/2) + 2

terms involving the same radical can be collected together just like x terms, x^2 terms, etc etc

  

Answer 2

1. root(24)=root(4*6)=2root(6)

2. root(54)=root(9*6)=3root(6)

3. root(a^5)=a^2root(a)