rationalising factor of 2⅓-1 is
Answers
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