Prove that√5 is a irrational number

Mathematics

2 answers:

SIZIF [17.4K]3 years ago

8 0

Answer:

The square root of five is 2.2360679775...

Step-by-step explanation:

The square root of five is irrational because it never ends (example: 3.1415... )

MAVERICK [17]3 years ago

6 0

Answer: 1. This irrationality proof for the square root of 5 uses Fermat's method of infinite descent: Suppose that √5 is rational, and express it in lowest possible terms (i.e., as a fully reduced fraction) as mn for natural numbers m and n. Then √5 can be expressed in lower terms as 5n − 2mm − 2n, which is a contradiction.

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4. Suppose P(A) = 0.48 and P(B) = 0.62. a. Can A and B be mutually exclusive? Why or why not. b. If A and B are independent, the

kenny6666 [7]

Answer:

Step-by-step explanation:

a) Two events A,B are said to be mutually exlusive if any of the following occurs.

- A and B have an empty intersection

- A= B^c and their union is the whole sample space

- P(A intersection B) =0

REcall the following formula

$P(A\cupB ) = P(A)+P(B)-P(A\cap B)$

Note that P(A) + P(B) = 1.1. Since the probability is always a number between 0 and 1, it must happen that $P(A\cap B) >0$ , otherwise, $A\cup B$ would have a probability greater than 1. Hence, A, B are not mutually exclusive.