Question

The number of integral terms in the expansion of (√3 + 8√5)^256 is

Answer 1

Use the formula, the general term in the expansion of $(a+b)^n$ is

$T_{r+1}=C(r,n)a^rb^{n-r},r=0,1,2,...,n$.

Using this formula, the general term in the expansion of

$(\sqrt{3} +8\sqrt{5} )^{256}$ is

$T_{r+1}=C(r,256)\sqrt{3}^r(8\sqrt{5})^{256-r},r=0,1,2,...,256$

The term $T_{r+1}$ is integral when,

$r,256-r$ are are even numbers. That is

When $r=0,2,4,...,254,256$.

The number of such $r$ is $128+1=129$.

Thus, the number of integral terms in the expansion of

$(\sqrt{3} +8\sqrt{5} )^{256}$ is $129$.

Answer 2

The correct answer is 33..

Step by step explanation: