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The proof is by the method of reductio ad absurdum. We start by assuming that sqrt(30) is rational. That means that it can be expressed in the form p/q where p and q are co-prime integers. Thus sqrt(30) = p/q. This can be simplified to 30*q^2 = p^2 Now 2 divides the left hand side (LHS) so it must divide the right hand side (RHS). That is, 2 must divide p^2 and since 2 is a prime, 2 must divide p. That is p = 2*r for some integer r. Then substituting for p gives, 30*q^2 = (2*r)^2 = 4*r^2 Dividing both sides by 2 gives 15*q^2 = 2*r^2. But now 2 divides the RHS so it must divide the LHS. That is, 2 must divide 15*q^2. Since 2 does not divide 15, 2 must divide q^2 and then, since 2 is a prime, 2 must divide q. But then we have 2 dividing p as well as q which contradicts the requirement that p and q are co-prime. The contradiction implies that sqrt(30) cannot be rational.
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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.
Is the square root of a 143 a irrational number?
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
Is the square root of 10 rational or irrational?
Square root of 10 is irrational.
Is the square root of 12.1 a rational number or irrational number?
irrational square root of 121 = 11 square root of 1.21 = 1.1 square root of 12.1 = 3.47...
Is the square root of 4.1 a rational or irrational number?
[ square root of (4.1) ] is irrational. But [ square root of (4) ] is rational.
Prove the square root of 2 not irrational?
This is impossible to prove, as the square root of 2 is irrational.
Is the square root of thirty-six an irrational?
No. The square root of thirty-six is positive or negative six.
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
What set does the square root of thirty belong to?
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.
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.
Is the square root of a 143 a irrational number?
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
Is they sqare root of 94 irrational or irrational?
The square root of 94 is an irrational number
Is the square root of 200 rational or irrational?
The square root of 200 is irrational.
Is the square root of 28 irrational or rational?
irrational
Is the square root of 11 rational or irrational?
The square root of 11 is irrational. An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. In the case of the square root of 11, it is a non-repeating, non-terminating decimal and cannot be simplified further. Therefore, it falls under the category of irrational numbers.
