Question

Which expression has an irrational answer?

Answer 1

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:

$\frac{65}{10}$

So, it is a rational number.

C) 2x^7

It can be written in p\q form:

$\frac{2x^7}{1}$

D) 1.25+ 4.25

which is equal to 5.50

It can be written in p\q form:

$\frac{55}{10}$

But,

B) $3x^\frac{1}{3}$ results irrational numbers as it can't be written in p\q form.

Hence, Option 'B' is correct.

Answer 2

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 × $\frac{1}{3}$

Since 3 is rational , but   $\frac{1}{3}$ is irrational. So product of rational and irrational should be irrational.

Because  $\frac{1}{3}$= 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

=$2 (a)^7$

= $a^7$ has denominator of the form other than $2^a or 5 ^b or (2 ^a \times 5 ^b)$ , then it is irrational number.

So, $2 (a)^7$ 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) $2 (a)^7$ may be irrational , it totally depends on the value of a.