Question

The rationalising factor of 2^1/3+2^-1/3

Answer 1

Answer:

The rationalizing factor is $2^{\frac{2}{3}}$

Step-by-step explanation:

Given Expression:

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

To find: Rationalizing factor

Rationalizing factor is the term which multiplied and divided to given expression so that the denominator has no rational number.

Consider,

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

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

$=\frac{2^{\frac{1}{3}}\times2^{\frac{1}{3}}+1}{2^{\frac{1}{3}}}$

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

From above  simplified expression,

The rationalizing factor = $2\div2^{\frac{1}{3}}=2^{\frac{2}{3}}$

Therefore, The rationalizing factor is $2^{\frac{2}{3}}$

Answer 2

Step-by-step explanation:

Answer:

The rationalizing factor is 2^{\frac{2}{3}}2

3

2

Step-by-step explanation:

Given Expression:

2^{\frac{1}{3}}+2^{\frac{-1}{3}}2

3

1

+2

3

−1

To find: Rationalizing factor

Rationalizing factor is the term which multiplied and divided to given expression so that the denominator has no rational number.

Consider,

2^{\frac{1}{3}}+2^{\frac{-1}{3}}2

3

1

+2

3

−1

=2^{\frac{1}{3}}+\frac{1}{2^{\frac{1}{3}}}=2

3

1

+

2

3

1

1

=\frac{2^{\frac{1}{3}}\times2^{\frac{1}{3}}+1}{2^{\frac{1}{3}}}=

2

3

1

2

3

1

×2

3

1

+1

=\frac{2^{\frac{2}{3}}+1}{2^{\frac{1}{3}}}=

2

3

1

2

3

2

+1

From above simplified expression,

The rationalizing factor = 2\div2^{\frac{1}{3}}=2^{\frac{2}{3}}2÷2

3

1

=2

3

2

Therefore, The rationalizing factor is 2^{\frac{2}{3}}2

3

2