Question

Total no of irrational terms in the expansion of (2^1/3+3^1/2+5^1/6)^10

Answer 1

The number of irrational terms in the expansion are 9

Step-by-step explanation:

$(2^1^/^3 + 3^1^/^2 + 5^1^/^6)^1^0$  is the  given equation.

By using BINOMIAL EQUATION

We  know that the power of expansion is n = 10

So the number of terms after expansion will be n + 1 = 11

For a term to be rational the powers of 2, 3  and 5 should be integral multiples of  $\frac{1}{3} , \ \frac{1}{2} \ and \ \frac{1}{6}$ respectively so as to cancel out the fractional exponents.

So for ratianalising  2, the powers should be = 0, 3, 6 and 9

For rationalising  3 , the powers should be = 0 , 2 , 4 , 6  and 8

For rationalising  5 , the powers should be = 0 and  6 .

The common powers for which the whole equation will be raional are = 0 and 6.

So two powers make ratinal terms so remaining   11 - 2 = 9 terms will be irrational.

$\textbf{\Large So, the number of irrational terms in the expansion are 9}$