PROOF :- Assume that the given real number is rational. This means that the number can be expressed in the form p/q where p and q belong to integers as well as are co-prime.

So,

3 + 2root5 = p/q

Or,

2root5 = p/q – 3 = (p -3q)/q Or,

Root5 = (p-3q)/2q ……. (i)

Now, (p-3q)/2q is a … (more)

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Carlos Eugenio Thompson Pinzón

, Triple IMO bronze medalist

Answered March 5, 2019

Rational numbers are a field and it is close to addition, subtraction, multiplication and division (except division by zero).

So let’s suppose that 3+25–√ is rational.

If 3+25–√ is rational, then (3+25–√)−3=25–√ is rational. And if 25–√ is rational, then 25–√÷2=5–√ would be rational.

Now, if 5–√ is rational, then there would exist to integers p,q such as 5–√=pq. If q is negative, then 5–√=−p−q for a positive integer −q. And, among all possible values of pq=5–√ with positive q there is one pair with the less possible positive q.

So let’s take … (more)

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Girija Warrier

, former Mathematics Teacher

Answered February 26, 2019

TO PROVE:( 3 + 2√5) is irrational

For proving this , we can apply the theorem “ √5 is an irrational number”

PROOF: Let (3 + √5 ) be a rational number.

=> 3+√5= p/q ( where, p & q are integers, ‘q’ not = 0 )

=> √5 = (p/q) -3

=> √5 = (p-3q)/q

Here, in RHS , numerator is the difference of 2 integers, which always remains an integer. & denominator is also an integer, not = 0.

=> RHS is a rational number ( as, all the conditions for being a rational number, have been satisfied )

But LHS is an irrational number. ( by theorem, √5 is an irrational number)

## Answers ( )

Answer:the answer is

Step-by-step explanation:So, let’s solve!!

TO PROVE :- 3+2root 5 is irrational.

PROOF :- Assume that the given real number is rational. This means that the number can be expressed in the form p/q where p and q belong to integers as well as are co-prime.

So,

3 + 2root5 = p/q

Or,

2root5 = p/q – 3 = (p -3q)/q Or,

Root5 = (p-3q)/2q ……. (i)

Now, (p-3q)/2q is a … (more)

4

0

0

Add Comment

View Collapsed Comments

Carlos Eugenio Thompson Pinzón

, Triple IMO bronze medalist

Answered March 5, 2019

Rational numbers are a field and it is close to addition, subtraction, multiplication and division (except division by zero).

So let’s suppose that 3+25–√ is rational.

If 3+25–√ is rational, then (3+25–√)−3=25–√ is rational. And if 25–√ is rational, then 25–√÷2=5–√ would be rational.

Now, if 5–√ is rational, then there would exist to integers p,q such as 5–√=pq. If q is negative, then 5–√=−p−q for a positive integer −q. And, among all possible values of pq=5–√ with positive q there is one pair with the less possible positive q.

So let’s take … (more)

4

1

0

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All about talent of kids

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Mathematical World !!

This space is dedicated to visualize beauty of mathematics.Have a nice time here

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198.8K

Mathematics is life

This space is dedicated to the beauty of mathematics.

Follow

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Mathematics(Use of mind)

This space is all about Mathematics

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This space is for who like to search happiness in life and for who love Maths

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The knowledge world

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Girija Warrier

, former Mathematics Teacher

Answered February 26, 2019

TO PROVE:( 3 + 2√5) is irrational

For proving this , we can apply the theorem “ √5 is an irrational number”

PROOF: Let (3 + √5 ) be a rational number.

=> 3+√5= p/q ( where, p & q are integers, ‘q’ not = 0 )

=> √5 = (p/q) -3

=> √5 = (p-3q)/q

Here, in RHS , numerator is the difference of 2 integers, which always remains an integer. & denominator is also an integer, not = 0.

=> RHS is a rational number ( as, all the conditions for being a rational number, have been satisfied )

But LHS is an irrational number. ( by theorem, √5 is an irrational number)

=> LHS not = RHS

=> our assumption (that 3+√5 is a ratio … (more)

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SusaiRaj

, former Retired Teacher.