Simplify the expression squareroot 27 c5 squareroot 3 squar

Simplify the expression (squareroot 27 c^5 + squareroot 3) (squareroot 27 c^5 - squareroot3). There should be no squareroot (s) in the answer.

Solution

( sqrt 27 c^5 + sqrt 3 ) ( sqrt 27c^5 - sqrt 3)

applying difference of squares formula

(a-b)(a+b) = a^2 - b^2

therefore ,

( sqrt 27 c^5 + sqrt 3 ) ( sqrt 27c^5 - sqrt 3) = (sqrt 27c^5)^2 - ( sqrt 3)^2

= 27c^5 - 3