Given:
A = sqrt(3)
B = 2sqrt(3)
c = sqrt(25)
D = sqrt(16)
Which expressions result in a rational number? Select all that apply
A + B
C + D
A + D
A x B
B x D
C x D
A x A
A + D
B x D
C x D
Explain
In order for an expression to result in a rational number, the square root terms must cancel out completely, leaving only integer terms.
A + D: sqrt(3) + sqrt(16) = sqrt(3) + 4 = a rational number
B x D: 2sqrt(3) x sqrt(16) = 2sqrt(3) x 4 = 8sqrt(3) = not a rational number
C x D: sqrt(25) x sqrt(16) = sqrt(25) x 4 = 5 x 4 = a rational number