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State True/False.

$52$ is irrational.

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True

False

answer is A.

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Detailed Solution

It is given to prove the number

52

is irrational.
Irrational numbers are the subset of real numbers, p/q, where p and q are integers, that cannot be stated as a fraction.
Let us assume that the number

52

is rational.
Then,

52 = a b

,where a and b are integers and have no common factors other than 1.

∴ 52 = a b ⇒ 2 = a 5 b

Since 5, a & b are integers,

a 5 b

is a rational number.

⇒

2

is rational number which is a contradiction, since

2

is an irrational number.

∴

Our assumption was wrong.
Hence,

52

is an irrational number.
Therefore,

52

is an irrational number is true.
Hence the correct option is 1.

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