Question

which of the following statements is true? a) both the square root of 0.25 and -the square root of 16 are irrational. b) the square root of 0.25 is rational and -the square root of 16 is irrational c) both the square root of 0.25 and -the square root of 16 are rational d) the square root of 0.25 is irrational and -the square root of 16 is rational

Answer 1

The answer is C because the only time a square root is irrational is if it is a negative like -16 it is irrational because you can’t have 4^2=4*-4

Answer 2

Option: C is the correct answer.

c) both the square root of 0.25 and -the square root of 16 are rational.

Explanation:

Rational Number--

A number which could be expressed in the form of p/q where p belongs to integers and q belongs to natural numbers.

and if it could not be expressed as one then the number is called a irrational number.

(1)

\sqrt{0.25}

Now, we can represent it as follows:

`√(0.25)=\sqrt{(25)/(100)}\\\\i.e.\\\\√(0.25)=\sqrt{((\pm 5)/(10))^2}\\\\i.e.\\\\√(0.25)=\pm (5)/(10)=\pm (1)/(2)`

Hence, the number could be expressed in the form of p/q

Hence, the number is a rational number.

2)

`-√(16)`

It could be represented as follows:

`-√(16)=-√((\pm 4)^2)\\\\i.e.\\\\-√(16)=\pm 4`

Hence, the number is a rational number.