Number of terms in expansion of {left( {√[4]{9} + √[6]{8}} right)^{500}} , which are inte

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7.Binomial Theorem

normal

The number of terms in the expansion of ${\left( {\sqrt[4]{9} + \sqrt[6]{8}} \right)^{500}}$, which are integers is

A

$501$

B

$251$

C

$42$

D

$41$

Solution

$\left(3^{\frac{2}{4}}+2^{\frac{3}{6}}\right)^{500}=\left(3^{\frac{1}{2}}+2^{\frac{1}{2}}\right)^{500}$

$\left[\frac{500}{2}\right]+1=251$

Standard 11

Mathematics

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