If x = 5 + 2√6, then the value of √x + 1 is,

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x = 5 + 2√6

∴	1	=	1	=	5 − 2√6
	x		5 + 2√6		(5 + 2√6)(5 − 2√6)

=	5 − 2√6	= 5 − 2√6
	25 − 24

∴		√x +	1		²	= x +	1	+ 2
			√x				x

= 5 + 2√6 + 5 – 2√6 + 2 = 12

∴	√x +	1	= √12 = 2√3
		√x