Prove that root 2 root 3 is irrational

Asked by admin @ in Math viewed by 333 People

Prove that root2 +root 3 is irrational

Answered by admin @


Solution:

Let us suppose that √2+√3 is rational.

Let √2+√3=\frac{a}{b},

where a,b are integers and b≠0

Therefore,

\sqrt{2}=\frac{a}{b}-\sqrt{3}

On Squaring both sides , we get

2=\frac{a^{2}}{b^{2}}+3-2\times\frac{a}{b}\times\sqrt{3}

Rearranging the terms ,

\frac{2a}{b}\times\sqrt{3}=\frac{a^{2}}{b^{2}}+3-2

= \frac{a^{2}}{b^{2}}+1

\sqrt{3}=\frac{a^{2}+b^{2}}{2ab}

Since , a,b are integers ,

\frac{a^{2}+b^{2}}{2ab} is rational, and so √3 is rational.

This contradicts the fact √3 is irrational.

Hence, √2+√3 is irrational.

•••••


Similar Questions

Prove that root 2 3 root 2 is irrational

Asked by admin @ in Math viewed by 306 persons

Prove that root2+3/root2 is an irrational no

Prove that 3 2 root 5 is irrational

Asked by admin @ in Math viewed by 326 persons

Prove that 3+2 root 5 is irrational

Prove that 3 2 under root 5 is irrational

Asked by admin @ in Math viewed by 316 persons

Prove that 3+2 root 5 is irrational

How to prove root 2 plus root 3 is irrational

Asked by admin @ in Math viewed by 290 persons

Prove that root 2 plus root3 is an irrational

Prove that 2 root 3 is an irrational number

Asked by admin @ in English viewed by 487 persons

How to prove 2+root3 is irrational number

Prove that root 3 2 root 5 is irrational

Asked by admin @ in Math viewed by 458 persons

Prove that root 3+2 root 5 is irrational

Prove that 2 root 3 by 5 is irrational

Asked by admin @ in Math viewed by 433 persons

Prove that 2 root 3 /5 is an irrational number

Prove that root 2 root 3 is irrational number

Asked by admin @ in Math viewed by 388 persons

Prove that root2 +root 3 is irrational

Prove that root 2 plus root 3 is irrational

Asked by admin @ in Math viewed by 347 persons

Prove that root2 +root 3 is irrational

Prove that 3 2 root 5 is irrational number

Asked by admin @ in Math viewed by 300 persons

Prove that 3+2 root 5 is irrational

Prove that 1 by root 2 is irrational

Asked by admin @ in Math viewed by 283 persons

Prove that 1/root 2 is irrational

Prove that root 2 is irrational class 10

Asked by admin @ in Math viewed by 287 persons

Prove that √2 is irrational. Class 10 - cbse

Prove that root 2 root 5 is irrational

Asked by admin @ in Math viewed by 308 persons

Prove that root 2 + root 5 is irrational

Prove that root 2 is an irrational number

Asked by admin @ in Math viewed by 264 persons

Proof that root 2 is irrational

Prove that root 3 root 5 is irrational

Asked by admin @ in Math viewed by 399 persons

Prove that root 3 plus root 5 is irrational

Most viewed questions in Math

What is the value of x in the expression

Asked by admin @ in Math viewed by 15151 persons

Shubham is facing south and moves 30 km

Asked by admin @ in Math viewed by 12987 persons

Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ in Math viewed by 12034 persons

Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ in Math viewed by 11518 persons

Survey of various types of bank accounts icse project

Asked by admin @ in Math viewed by 11506 persons

The town of p is located at point x

Asked by admin @ in Math viewed by 11359 persons

A clock gains 4 minutes after every 4 minutes

Asked by admin @ in Math viewed by 10167 persons

Running a tuck shop or canteen maths project pdf

Asked by admin @ in Math viewed by 9379 persons

Paul is sixteenth from the front of the row

Asked by admin @ in Math viewed by 9352 persons

The average weight of 20 teachers is 80 kg

Asked by admin @ in Math viewed by 7524 persons

The number 567 xy is completely divisible by 30

Asked by admin @ in Math viewed by 7396 persons

In a row of friends tiya occupies fifteenth place

Asked by admin @ in Math viewed by 7207 persons

What would $ mean if fat is coded as

Asked by admin @ in Math viewed by 5275 persons

Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4804 persons

Rahul went to his mother's mother in law

Asked by admin @ in Math viewed by 4179 persons