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The proof is by the method of reductio ad absurdum. We start by assuming that cuberoot(7) is rational. That means that it can be expressed in the form p/q where p and q are co-prime integers. Thus cuberoot(7) = p/q. This can be simplified to 7*q^3 = p^3 Now 7 divides the left hand side (LHS) so it must divide the right hand side (RHS). That is, 7 must divide p^3 and since 7 is a prime, 7 must divide p. That is p = 7*r for some integer r. Then substituting for p gives, 7*q^3 = (7*r)^3 = 343*r^3 Dividing both sides by 7 gives q^3 = 49*r^3. But now 7 divides 49 so 7 divides the RHS. Therefore it must divide the LHS. That is, 7 must divide q^3 and since 7 is a prime, 7 must divide q. But then we have 7 dividing p as well as q which contradicts the requirement that p and q are co-prime. The contradiction implies that cuberoot(7) cannot be rational.
What else can I help you with?
Is cube root of negative nine terminates?
No, the cube root of -9 is an irrational number.
Prove that square root of 2 is an irrational number?
The square root of 2 is 1.141..... is an irrational number
How can you prove that the square root of three is an irrational number?
Because 3 is a prime number and as such its square root is irrational
Is the cube root of 30 rational?
No, it is irrational.
What cubed equals 72?
The cube root of 72 is an irrational number; to 3 decimal places it is 4.160.
Is cube root of negative nine terminates?
No, the cube root of -9 is an irrational number.
Prove that square root of 2 is an irrational number?
The square root of 2 is 1.141..... is an irrational number
How can you prove that the square root of three is an irrational number?
Because 3 is a prime number and as such its square root is irrational
Can you cube an irrational number to form a rational number?
sure , take cube root of 3, that is irrational, but when you cube it you have 3 which is clearly rational! Doctor Chuck aka mathdoc
Prove the square root of 2 not irrational?
This is impossible to prove, as the square root of 2 is irrational.
How do you prove that root 2 root 3 is an irrational number?
It is known that the square root of an integer is either an integer or irrational. If we square root2 root3 we get 6. The square root of 6 is irrational. Therefore, root2 root3 is irrational.
What are the examples of irrational numbers?
The square root of any number which is not a perfect square;The cube root of any number which is not a perfect cube;Pi, the circular constant.e, the natural logarithm base number.
Is the cube root of 30 rational?
No, it is irrational.
Is the cube root always a whole number?
"Most of the time" is somewhat problematic, since we are dealing with infinite sets of numbers. But it is tempting to say that. The fact is, any number can be a cube root, since you can cube any number by multiplying it by itself twice. But the cube root of a whole number is always either a whole number or an irrational number. And it is true that if N is any reasonably large whole number (say, 1000 or more), the majority (in fact, at least 99%) of the whole numbers from 1 to N have irrational cube roots.Answer 1No. Most of the time it's an irrational number.
Is the square root of 6 rational?
No; you can prove the square root of any positive number that's not a perfect square is irrational, using a similar method to showing the square root of 2 is irrational.
Prove that root 2 is irrational number?
I linked a good resource that explains what you asked below.
What cubed equals 72?
The cube root of 72 is an irrational number; to 3 decimal places it is 4.160.
