prove that √3 is irrational number
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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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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:
√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...