Question

Which will multiple with 2^1/3 so that it will become rational number

Answer 1

Answer

As per your question we are given $\rm 2^ \frac { 1 } { 3 }$ and we need to rationalize it.

Condition given is We have to only multiply it by other number to do so.

We know that if bases are same when multiplying then the exponents adds up.

Now,

We need a positive integer as the exponent.

So, we can multiply the given number by $\rm 2^ \frac { 5 } { 3 }$

$\implies \rm 2^ \frac { 1 } { 3 }$ × $\rm 2^ \frac { 5 } { 3 }$

As bases are same we can just add up exponents.

We get,

$\implies \rm 2^ \frac { 6 } { 3 }$

$\implies \rm 2^2$

Surely we got a rational number...

So we need to multiply the given number by $\rm 2^ \frac { 5 } { 3 }$. so as to rationalize it.