## Find an irrational number between 2root 3 and 3root 5

Question

Find an irrational number between 2root 3 and 3root 5

in progress 0
3 days 2021-10-11T15:53:26+00:00 1 Answer 0 views 0

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

Carlos Eugenio Thompson Pinzón

, Triple IMO bronze medalist

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

If you are a small business, we are here to help.

A Dell advisor is standing by, ready to get you the technology solutions you need.

The Math Guru

School Maths CBSE, ICSE, IB and Quantitative Aptitude Questions, Math shortcuts

Follow

19.4K

Learn Mathematics Skills

Everything about Mathematics – Learn/Simplify/Tips/Easy Methods

Follow

12.6K

Zons19

Follow

4

Mathematical World !!

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

Follow

198.8K

Mathematics is life

This space is dedicated to the beauty of mathematics.

Follow

28.6K

Mathematics(Use of mind)

This space is all about Mathematics

Follow

16.9K

Mathemagics & Puzzles

Vedic Mathematics, Quantitative Aptitude Q&A, Puzzles, Facts and more.

Follow

25.6K

MATHS HOMEWORK HELP

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

Follow

3.9K

The knowledge world

This is the most popular space for everyone. Join and share your experience here

Follow

35.3K

Science & Maths sprinters

This group contain knowledge related to Science ,Mathematics and more subjects..

Follow

52.1K

View More Spaces

Girija Warrier

, former Mathematics Teacher

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)

2

0

0