If x = 7 – 4√3 , then √x + 1

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x = 7 – 4√3
∴ √x = √7 – 4√3
= √7 – 2 × 2 × √3
= √4 + 3 − 2 × 2 × √3
= √(2 − √3)² = 2 − √3

∴	1	=	1
	√x		2 − √3

=	1	×	2 + √3	=	2 + √3
	2 − √3		2 + √3		4 − 3

= 2 + √3

∴ √x +	1	= 2 − √3 + 2 + √3 = 4
	√x