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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
What else can I help you with?
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.;
Is the square root of 128 irrational?
The square root of 128 is not an irrational number; it can be simplified. Specifically, (\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}). Since (\sqrt{2}) is irrational, (\sqrt{128}) is also 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)
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 square root of 128 irrational?
The square root of 128 is not an irrational number; it can be simplified. Specifically, (\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}). Since (\sqrt{2}) is irrational, (\sqrt{128}) is also irrational.
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.
Is every irrational a surd?
sqrt(8) = /(8) = sqrt(2 x 4) => sqrt(2 x4) = sqrt(2) X sqrt(4) => sqrt(2) X 2 => 2*sqrt(2) '2' is a Prime Number. The 'Square Roots' of prime numbers are IRRATIONAL. sqrt(2) = 1.414213562.... ( to infinity). This makes it irrational . Hence 2 * 1.414213562.... = 2.828427125..... (Which is also irrational). NB A rational number multiplied to an irrational number produces an irrational result,.
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.
