It is an irrational number because it can't be expressed as a fraction
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.
- sqrt(26)
It is an irrational number and it is 12 times the square root of 26
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.
the square root of 26 is a irrational number
2.6 is the ratio of 26 to 10 ... nice and rational.
It is an irrational number because it can't be expressed as a fraction
It is an irrational number because it can't be expressed as a fraction
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.
It is a rational number because it can be expressed as a fraction in the form of 26/5
Yes it is.
Yes
-sqrt(26)
26 is an integer and not a fraction. However, it can be expressed in rational form as 26/1. You can then calculate equivalent rational fractions if you multiply both, its numerator and denominator, by any non-zero integer.
No, it is a rational number. It that is meant to be the terminating decimal 0.1575757: 0.1575757 = 1575757/10000000 If that is meant to be the recurring decimal 0.1575757... with the 57 repeating forever: 0.1575757... = 1/10 + 57/990 = 156/990 = 26/165
- sqrt(26)