Proof that 3 – \sqrt{8} is irrational.

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2 thoughts on “Proof that 3 – \sqrt{8} is irrational.<br /><br />→Need quality answer.​”

1. Step-by-step explanation:

   Given :–

   3-√8

   To find :–

   Prove that 3-√8 is an irrational number ?

   Solution :–

   Given that :

   3-√8

   It can be written as 3-√(2×2×2)

   => 3 – 2√2

   Let us assume that

   3 – 2√2 is a rational number

   It must be in the form of p/q , where p and q are integers and q ≠ 0

   Let 3-2√2 = a/b

   Where a and b are co-primes

   => -2√2 = (a/b) -3

   => 2√2 = 3-(a/b)

   => 2√2 = (3b-a)/b

   => √2 = (3b-a)/(2×b)

   => √2 = (3b-a)/2b

   =>√2 is in the form of p/q

   => √2 is a rational number

   But We know that

   => √2 is not a rational number.

   => √2 is an irrational number

   This contradicts to our assumption that (3-√8) is a rational number.

   3-√8 is not a rational number.

   3-√8 is an irrational number.

   Hence, Proved.

   Answer:–

   3-√8 is an irrational number.

   Note :-

   3 is a rational number

   √8 is an irrational number

   The difference between the rational and irrational is also an irrational number.

   3-√8 is an irrational number.

   Used Method :–

   • Method of Contradiction or Indirect method

   Points to know :–

   • The numbers are in the form of p/q ,where p and q are integers and q≠0 called rational numbers. They are denoted by Q.

   • The numbers are not in the form of p/q ,where p and q are integers and q≠0 called irrational numbers. They are denoted by Q’ or S.

   • If q is the rational number and s is the irrational number then

   • q+s is an irrational number.

   • q-s is an irrational number.

   • q×s is an irrational number.

   • q/s is an irrational number.

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2. Answer:

   In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

   Step-by-step explanation:

   Bestu Pata ha jub koiye apna rooth jata ha na tub aise he shoulder per head rakhta ha aur jo apna hota ha na wo bahut sad hota ha rota raheta ha bus bol nhi pata wo use samjhata hu ke pagal tere bina mera aur hai he kon agar Tu sad rahage to mai khush kaise raha sakta hu tere bina yeh zindage adhura hai tu he mere sab kuch ha.dp acha ha na mera usme mera family member ha matlab samjhe na( bestu family member)

   aur maine use apne shoulder par head rakh kar chup karaiya.ಥ‿ಥ aur mat ro bestu.

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