If we assume that the sqare root of 5 is a rational number, then we can write it as a/b in its simplest form, where a and b have no common factors.
Therefore 5 = a2/b2
Therefore 5b2 = a2
Therefore a2 is divisible by 5, because b2 is an integer
Therefore a is divisible by 5, because 5 is a Prime number.
Therefore 5 = 5c/b, where c is an integer
Therefore 1 = c/b
Therefore c = b
Therefore sqrt 5 = 5c/c = 5, which is impossible.
So sqrt5 cannot be expressed in the form a/b, and is irrational.
5
It is root 3.
5 times the square root of 3
Two ways: Find the square root first. If it's a whole number, find the prime factorization like you would for any other number. Or, find the prime factorization of the original number. The factors will be paired. Take one out of of each pair. Example: 900 The square root of 900 is 30. The prime factorization of 30 is 2 x 3 x 5 or The prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5 The square root will be 2 x 3 x 5, or 30
X^2 + 5 doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: 0 plus or minus i times the square root of 5.x = 0 + 2.23606797749979ix = 0 - 2.23606797749979iwhere i is the square root of negative one.
Root signs didn't show up
They are +5 and -5, which are both rational.
You cannot. The square root of 5 is irrational.
The square root of 5 is an irrational number
7 plus the square root of 5 is an irrational number because the square root of 5 is a never ending decimal number that can't be expressed as a fraction.
The square root of (any number that isn't a perfect square) is irrational.
Irrational
Yes.
Yes, they are.
Yes.
Square root of 2, square root of 3, square root of 5, pi, e
Yes, the square root of 125 is an irrational number. It can be simplified to ( 5\sqrt{5} ), where ( \sqrt{5} ) is an irrational number. Since the product of a rational number (5) and an irrational number ((\sqrt{5})) is irrational, ( \sqrt{125} ) is also irrational.