Give an example of a number x such that $x^{2}$ is an irrational number and $x^{4}$ is a rational number.

Open in App

Solution

$L e t x = \sqrt[4]{2} x^{2} = (\sqrt[4]{2})^{2} = (2^{\frac{1}{4}})^{2} = 2^{\frac{1}{2}} = \sqrt{2}, i r r a t i o n a l x^{4} = (\sqrt[4]{2})^{4} = (2^{\frac{1}{4}})^{4} = 2, r a t i o n a l$

Suggest Corrections

Similar questions

Q. Give an example of an irrational number such that its

8^{t h}

power is a rational number.

Let $x$ be a rational number and $y$ be an irrational number. Is $x + y$ necessarily an irrational number ? Give an example in support of your answer.

Can u give an example to show that the product of a rational number and an irrational number may be a rational number?

Q. Give an example of each, of two irrational numbers whose:
(i) difference is a rational number.
(ii) difference is an irrational number.
(iii) sum is a rational number.
(iv) sum is an irrational number.
(v) product is an rational number.
(vi) product is an irrational number.
(vii) quotient is a rational number.
(viii) quotient is an irrational number.

Is the product of a rational and an irrational number always irrational? Give an example

Join BYJU'S Learning Program

Give an example of a number x such that x2 is an irrational number and x4 is a rational number.

Let x=4√2x2=(4√2)2=(214)2=212=√2, irrationalx4=(4√2)4=(214)4=2, rational

Give an example of a number x such that $x^{2}$ is an irrational number and $x^{4}$ is a rational number.

$L e t x = \sqrt[4]{2} x^{2} = (\sqrt[4]{2})^{2} = (2^{\frac{1}{4}})^{2} = 2^{\frac{1}{2}} = \sqrt{2}, i r r a t i o n a l x^{4} = (\sqrt[4]{2})^{4} = (2^{\frac{1}{4}})^{4} = 2, r a t i o n a l$