If 4√3 + 5√2 = a + b√6,

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L.H.S. =	4√3 + 5√2
	√48 + √18

=	4√3 + 5√2
	4√3 + 3√2

=	4√3 + 5√2	×	4√3 − 3√2
	4√3 + 3√2		4√3 − 3√2

(Rationalising the denominator)

=	16 × 3 − 12 √6 + 20√6 −15 × 2
	(4√3)² − (3√2)²

=	48 + 8√6 − 30
	48 − 18

=	18 + 8√6	=	9	+	4√6
	30		15		15

=	3	+	4√6
	5		15

Now,	3	+	4√6	= a + b√6
	5		15

∴ a =	3	and b =	4
	5		15

If	4√3 + 5√2	= a + b√6, then the values of a and b are respectively
	√48 + √18