(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\), a and b are positive integers. Find the value…

Explanation

(\(\sqrt{a} +\sqrt{8a})^2\) =  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.

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