0
Still curious? Ask our experts.
Chat with our AI personalities
Beau
Rene
Maxine
Add your answer:
Earn +20 pts
Is the square root of 26 rational or irrational?
It is an irrational number because it can't be expressed as a fraction
Is 6 square root of 26 rational number?
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
What is an example of an irrational number less than -5?
- sqrt(26)
What is the Square root of 3744?
It is an irrational number and it is 12 times the square root of 26
To prove cube root of 26 is irrational?
The proof is by the method of reductio ad absurdum. We start by assuming that cuberoot of 26, cbrt(26), is rational. That means that the cube root can be expressed in the form p/q where p and q are co-prime integers. That is, cbrt(26) = p/q.Therefore, p^3/q^3 = 26 which can also be expressed as 26*q^3 = p^3 Now 26 = 2*13 so 2 divides the left hand side (LHS) and therefore it must divide the right hand side (RHS). That is, 2 must divide p^3 and since 2 is a prime, 2 must divide p. That is p = 2*r for some integer r. Then substituting for p gives, 26*q^3 = (2*r)^3 = 8*r^3 Dividing both sides by 2 gives 13*q^3 = 4*r^3. But now 2 divides the RHS so it must divide the LHS. That is, 2 must divide q^3 and 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 cbrt(26) cannot be rational.
