Simplify Assume the variable represents a nonnegative real n

Simplify. Assume the variable represents a nonnegative real number. squareroot 98x - squareroot 108x + squareroot 12x squareroot 98x - squareroot 108x + squareroot 12x = (Type an exact answer, using radicals as needed. Simplify your answer.)

Solution

sqrt (98x) - sqrt (108x) + sqrt (12x)

sqrt (98x) = sqrt ( 2*7*7*x ) = 7 sqrt (2x)

sqrt (108x) = sqrt ( 2*2*3*3*3*x ) = 6 sqrt (3x)

sqrt (12x) = sqrt ( 2*2*3*x ) = 2 sqrt(3x)

therefore, expression becomes

7 sqrt (2x) - 6 sqrt (3x) + 2 sqrt(3x)

7 sqrt (2x) - 4 sqrt (3x)