Question

The rationalising factor for 16^1/3 + 4^1/3 + 1 is
Please answer with explanation
Please..

Answer 1

i hope u understand very well

Answer 2

Answer:

The solution of the given expression is 3.

Step-by-step explanation:

Given : Expression $16^{\frac{1}{3}}+4^{\frac{1}{3}}+ 1$

To find : The rationalizing factor of the given expression?

Solution :

Expression $16^{\frac{1}{3}}+4^{\frac{1}{3}}+ 1$

To solve the given expression multiply it by $4^{\frac{1}{3}}-1$

$=(4^{\frac{1}{3}}-1)16^{\frac{1}{3}}+4^{\frac{1}{3}}+ 1$

$=(4^{\frac{1}{3}})(16^{\frac{1}{3}}+4^{\frac{1}{3}}+ 1)-1(16^{\frac{1}{3}}+4^{\frac{1}{3}})$

$=4^{\frac{1}{3}}\times 4^2^{\frac{1}{3}}+4^{\frac{1}{3}}\times4^{\frac{1}{3}}+4^{\frac{1}{3}}\times 1-16^{\frac{1}{3}}-4^{\frac{1}{3}}+1)(-1)$

$=4^{\frac{1}{3}+\frac{2}{3}}+4^{\frac{2}{3}}+4^{\frac{1}{3}}-4^{\frac{2}{3}}-4^{\frac{1}{3}}-1$

$=4^{1}-1$

$=4-1$

$=3$

Therefore, The solution of the given expression is 3.