# Find the value of x if √(1 + 33/256) = [1 + x/16]

**Answer: (1) 1 **

**Solution:-**

sqrt.(1 + 33/256) = [1 + X/16]

Square on both side,

(1 + 33/256) = [1 + X/16]^{2}

1 + 33/256 = 1 + (X/16)^{2} + 2 x 1 x X/16

33/256 = X^{2}/256 + X/8

X^{2}/256 + X/8 – 33/256 = 0

(X^{2} + 32 X – 33)/256 = 0

X^{2} + 32 X – 33 = 0

X^{2} + 32 X – 33 = 0

X^{2} + 32 X – 33 = 0

X^{2} + 33 X – X – 33 = 0

X (X + 33) – 1 (X + 33) = 0

(X – 1) (X + 33) = 0

X – 1 = 0

X = 1

Then, the value of X is 1.

Hence, the correct answer is option (1) 1.