Is it correct to say that there is a number x such that x 2 is irrational but x 4 is rational justify your answer by an example?

Answer: yes there are so many no. example 2^(1/4) which is irrational and its square is 2^(1/2) which is also irrational but again squaring it becomes 2 which is rational no.

Is X 2 and X 4 are rational?

For example, if x is the fourth root of 2, then x^2 is equal to the square root of 2, which is irrational, but x^4 is equal to 2 , which is rational. Yes, in general there is at least one such number.

Is x 2 an irrational number?

X squared is then the ratio of A squared to B squared, contradicting the premise that X squared is irrational. This proves the statement that X is irrational indirectly by proving the contraposition (that all non-irrational number can not be X).

Is X 2 is a rational number?

If x is 3+root2, then x^2 cannot be rational. So, if x is rational, then it’s square can be rational or irrational.

Is there a number a such that a 2 is irrational but a 4 is rational?

Is there a number a such that a2 is irrational, but a4 is rational? This problem is from Spivak Calculus, now you immediately think a2=√2 and a4=2, so the answer to the problem is yes.

Is 4 irrational or rational?

4 is a rational number because it can be expressed as the quotient of two integers: 4 ÷ 1.

Is Root 4 rational or irrational?

Is the Square Root of 4 Rational or Irrational? A number that can be expressed as a ratio of two integers, i.e., p/q, q = 0 is called a rational number. Now let us look at the square root of 4. Thus, √4 is a rational number.

How do you prove 2 is irrational?

Proof that root 2 is an irrational number.

1. Answer: Given √2.
2. To prove: √2 is an irrational number. Proof: Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q≠0. √2 = p/q.
3. Solving. √2 = p/q. On squaring both the sides we get, =>2 = (p/q)2

Is the sum of 2 irrational numbers irrational?

“The sum of two irrational numbers is SOMETIMES irrational.” The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Can x^2 be irrational but x^4 is rational?

There is a number x such that x^2 is irrational but x^4 is rational. Justify your answer by an example. – Sarthaks eConnect | Largest Online Education Community There is a number x such that x^2 is irrational but x^4 is rational. Justify your answer by an example. There is a number x such that x2 is irrational but x4 is rational.

How to identify rational and irrational numbers?

Let us see how to identify rational and irrational numbers based on below given set of examples. As per the definition, The rational numbers include all integers, fractions and repeating decimals. For every rational number, we can write them in the form of p/q, where p and q are integers value.

Is the sum of two rational numbers always rational?

#Rule 1: The sum of two rational numbers is also rational. #Rule 2: The product of two rational number is rational. #Rule 3: The sum of two irrational numbers is not always irrational. #Rule 4: The product of two irrational numbers is not always irrational.

Can irrational numbers be written in decimals?

Now, let us elaborate, irrational numbers could be written in decimals but not in the form of fractions, which means it cannot be written as the ratio of two integers. Irrational numbers have endless non-repeating digits after the decimal point. Below is an example of the irrational number: Example: √8 =2.828…