Question

prove that √3 is irrational number​

Answer 1

Step-by-step explanation:



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9th

Maths

Number Systems

Irrational Numbers

Prove that √(3) is an irrat...

MATHS

Prove that 3 is an irrational number. Hence, show that 7+23 is also an irrational number.

December 27, 2019Pintu Ganeshan

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ANSWER

Solution:

If possible , let 3 be a rational number and its simplest form be 

ba then, a and b are integers having no common factor 

other than 1 and b=0.

Now, 3=ba⟹3=b2a2    (On squaring both sides )

or, 3b2=a2         .......(i)

⟹3 divides a2   (∵3 divides 3b2)

⟹3 divides a

Let a=3c for some integer c

Putting a=3c in (i), we get

or, 3b2=9c2⟹b2=3c2

⟹3 divides b

Answer 2

Answer:

√3 is an irrational number because this for we convert it in to number or decimal form the result would be 1.732...... so it is an recurring number or terminating number so think type of number is called irrational number.....

Hence it has been proven...