Solution:
A number is said to be irrational , if the decimal expansion of a number is non terminating non repeating.
For example , 2.01001000100001......., √3,∛5,....
Now coming to Options
(A) 4 + 2.5
4 as well as 2.5 is rational . So sum of two rational is a rational.
(B) 3 × [tex]\frac{1}{3}[/tex]
Since 3 is rational , but [tex]\frac{1}{3}[/tex] is irrational. So product of rational and irrational should be irrational.
Because [tex]\frac{1}{3}[/tex]= 0.333333.......(non terminating non repeating)
But numerator which is 3 and denominator which is 3 cancels out and result is 1 which is rational number.
(C) 2 × (real number=a )raised to power of 7
=[tex]2 (a)^7[/tex]
= [tex]a^7[/tex] has denominator of the form other than [tex]2^a or 5 ^b or (2 ^a \times 5 ^b)[/tex] , then it is irrational number.
So, [tex]2 (a)^7[/tex] is rational or irrational depends on the value of a.
(D) 1.25 + 4.25
Both 1.25 as well as 4.25 are rational. So their sum is rational.
So, option (C) [tex]2 (a)^7[/tex] may be irrational , it totally depends on the value of a.
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
A) 4+2.5
which is equal to 6.5, which can be written in p\q form:
[tex]\frac{65}{10}[/tex]
So, it is a rational number.
C) 2x^7
It can be written in p\q form:
[tex]\frac{2x^7}{1}[/tex]
D) 1.25+ 4.25
which is equal to 5.50
It can be written in p\q form:
[tex]\frac{55}{10}[/tex]
But,
B) [tex]3x^\frac{1}{3}[/tex] results irrational numbers as it can't be written in p\q form.
Hence, Option 'B' is correct.
