(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\), a and b are positive integers. Find the value of a and the value of b.
A
a = 24, b = 6
B
a = 6, b = 2
C
a = 6, b = 24
D
a = 2, b = 6
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\)
(\(\sqrt{a} + \sqrt{8a}\))(\(\sqrt{a} + \sqrt{8a}\))
a + 4a\(\sqrt{2} + 8a = 54 + b\sqrt{2}\)
9a + 4a\(\sqrt{2}\) = 54 + b\(\sqrt{2}\)
comparing both sides
9a = 54, so that a = 6
4a = b
b = 4 x 6 = 24.
Source: Myschool Past Questions Archive (Record #71530)