Question

(3)ki power 1/3 is not a rational number​

Answer 1

Answer:

no its in a form of rational no.

Step-by-step explanation:

because this is in the form of p/q and q not equal to 0

Answer 2

we can conclude that $3^{1/3}$ is not a rational number and must be an irrational number.

The cube root of any non-zero integer is either a rational or irrational number. In the case of the expression $3^{1/3}$, we can use the Rational Root Theorem to determine whether it is rational or irrational.

Suppose that $3^{1/3}$ is a rational number. Then we can write it in the form p/q, where p and q are integers with no common factors. Cubing both sides, we get:

$3 = (p/q)^3 = p^3/q^3$

Multiplying both sides by $q^3$, we get:

$3q^3 = p^3$

This implies that $p^3$ is a multiple of 3. Since 3 is a prime number, this means that p must be a multiple of 3 as well. Let $p = 3k$for some integer k. Substituting this into the previous equation, we get:

$27k^3 = 3q^3$

Dividing both sides by 3, we get:

$9k^3 = q^3$

This implies that $q^3$ is a multiple of 9, which means that q must be a multiple of 3 as well. But this contradicts our assumption that p and q have no common factors, so we have reached a contradiction.

for such more question on rational number

https://brainly.in/question/135903

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