Question

What is the integral part of (√3 + 1)^8?

(a) 1558

(b) 1551

(c) 1552

(d) 1556

The question was posed to me during an interview for a job.

This question is from Binomial Theorem for Positive Integral Index in division Binomial Theorem of Mathematics – Class 11

Answer 1

The correct choice is (c) 1552

To explain I would say: By binomial expansion,

(√3 + 1)^7 = \(\Sigma_{r = 0}^{r = 7}\)(7Cr √3^7 – r (1)^r)

Whenever, r is an even number, 8 – r will also be even. Then √3 will also have an even power and thereby be integral.

Integral parts = 8C0 (√3)^0 + 8C2 (√3)^2 + 8C4 (√3)^4 + 8C6 (√3)^6 + 8C8 (√3)^8

Integral parts = 1 + 28 x 3 + 70 x 9 + 28 x 27 + 1 x 81

Integral part = 1552.