(i)Find whether variable x represent rational number or an irrational number.x2 = 5
(ii)Find whether variable x represent rational number or an irrational number.y2 = 9
(iii)Find whether variable x represent rational number or an irrational number.z2 = 0.04
(iv)Find whether variable x represent rational number or an irrational number.u2 =
(i)Answer. [Irrational]
Solution.
Given that
x2 = 5
On taking square root on both sides, we get
Irrational numbers are real numbers which cannot be represented as simple fractions.
So, x is an irrational number
(ii)Answer. [Rational]
Solution.
We have
y2 = 9
On taking square root on both sides, we get
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q
should be rational when the fraction is expressed in the simplest form.
So, y can be written as where 1, 3, -3 are rational numbers.
Hence y is rational.
(iii)Answer. [Rational]
Solution.
We have
z2 = 0.04 =
On taking square root on both sides, we get
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q
should be rational when the fraction is expressed in the simplest form.
So, z can be written as where 1, 5, -5 are rational numbers.
Hence z is rational.
(iv)Answer. [Irrational]
Solution.
Given that
u2 =
On taking square root on both sides, we get
Any number which can be represented in the form of p/q where q is not equal to zero
is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
So, u can be written as where is irrational.
Hence u is irrational.