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First we will assume that sqrt(2) is rational, meaning that it can be written as a ratio of two integers say (p/q) p and q must have no common factors sqrt(2)=p/q, square both sides 2=p^2/q^2, multiply both sides by q^2 2q^2=p^2, since 2 divides by the LHS, so does the RHS, meaning that p^2 is evenand because p^2 is even, so is p itselfLet p=2r with r being an integer so that p^2=2q^2=(2r)^2=4r^ 2Since 2q^2=4r^2, q^2=2r^2Because q^2 is 2r^2, then q^2 is even, meaning q itself is evenSince p and q are even, they have a common factor of 2THEREFORE, sqrt(2) cannot be rational
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Is an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
Are the product of irrational always is irrational?
No. Sqrt(2)*sqrt(18) = 6.
What is a rational number multiplied by an irrational number equal?
It can be a rational number or an irrational number. For example, sqrt(2)*sqrt(50) = 10 is rational. sqrt(2)*sqrt(51) = sqrt(102) is irrational.
Two irrational number whose sum is an irrational number?
Sqrt(2) and sqrt(3)
Why is phi an irrational number?
phi = [1+sqrt(5)]/2 sqrt(5) is irrational and so phi is irrational.
Is an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
Can you add two positive irrational numbers to get an irrational number?
Yes. sqrt(2) + sqrt(2) = 2*sqrt(2), an irrational number.
How can be the product of 2 irrational numbers a rational numbers 5?
5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!
Is a rational number times a irrational number?
Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]
Is the sum of irrational roots irrational?
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
If you divide 2 irrational numbers is the answer always an irrational number?
No, not always. For example, sqrt(2) is irrational (1.41421...), but sqrt(2)/sqrt(2) = 1. 1 is a rational number. Similarly, 2*sqrt(2) is irrational (2.82842...), but sqrt(2)/(2*sqrt(2)) = 1/2. 1/2 is a rational number.
Can you multiply two irrational numbers and get an irrational number?
Yes, but not always. An easy example is sqrt(2)*sqrt(3), which is sqrt(6) and irrational. An easy counterexample is simply sqrt(2) * sqrt(2), which is 2 and rational.
Is the sum of three irrational numbers an irrational number?
Yes, but not always. An easy example is sqrt(2) + sqrt(2) + sqrt(2) = 3sqrt(2), an irrational number. An easy counterexample is 2sqrt(2) + -sqrt(2) + -sqrt(2) = 0, which is rational.
Will any irrational number divided by an irrational number be irrational?
No.3*sqrt(2) and sqrt(2) are irrational. But their quotient is 3, which is rational.
Are the product of irrational always is irrational?
No. Sqrt(2)*sqrt(18) = 6.
What is a rational number multiplied by an irrational number equal?
It can be a rational number or an irrational number. For example, sqrt(2)*sqrt(50) = 10 is rational. sqrt(2)*sqrt(51) = sqrt(102) is irrational.
Does an irrational number multiplied by an irrational number equal an irrational number?
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
