Question

3. Raju said that the distance between (3,2) and (2,3)
is a rational number. But
pavan said that it is
irrational number with which do you agree
and why?​

Answer 1

Answer:

the answer is

$\sqrt{2}$

it is irrational number

Step-by-step explanation:

x1=3 , x2=2 , y1=2 , y2=3

by distance formula:

$= \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {(2 - 3)}^{2} + {(3 - 2)}^{2} } \\ = \sqrt{ {( - 1)}^{2} + {(1)}^{2} } \\ = \sqrt{ 1 + 1} = \sqrt{2}$

=>it irrational number. it can't be represented in the form of p/q , wher p and q are integers and q is not equal to 0

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Answer 2

Step-by-step explanation:

Given :-

Raju said that the distance between (3,2) and (2,3)

is a rational number. But Pavan said that it is

irrational number .

To find:-

with which do you agree? and why?

Solution:-

I agree with Pavan .

Reason:-

Given points are : (3,2) and (2,3)

Let (x1, y1)= (3,2)=>x1=3 and y1 =2

Let (x2, y2)=(2,3)=>x2=2 and y2=3

We know that

The distance between two points( x1 ,y1) and( x2 ,y2) is√[(x2-x1)^2+(y2-y1)^2] units

=>√[(2-3)^2+(3-2)^2] units

=>√[(-1)^2+(1)^2] units

=>√(1+1) units

=>√2 units

The distance between the two points = √2 units

We know that by the definition of an Irrational number-Let 'n' is a prime number then √n is an irrational number fore every natural number .

So, √2 is an irrational number.

Solution:-

I agree with Pavan .

√2 is an irrational number.

Used formulae:-

• The distance between two points( x1 ,y1) and( x2 ,y2) is√[(x2-x1)^2+(y2-y1)^2] units
• Let 'n' is a prime number then √n is an irrational number fore every natural number .
• The numbers are not in the form of p/q where p and q are integers and q≠0 called irrational Numbers
• Example:√2,√3,π,log2 ....