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  • (i)Find whether variable x represent rational number or an irrational number. xsquare 2 = 5

(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 = \frac{17}{4}

Answers (1)

(i)Answer.          [Irrational]
Solution.        
Given that
x2 = 5
On taking square root on both sides, we get
\Rightarrow x= \pm \sqrt{5}
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
\Rightarrow x= \pm 3

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 \frac{3}{1},\frac{-3}{1} where 1, 3, -3 are rational numbers.
Hence y is rational.

(iii)Answer.          [Rational]
Solution.        
We have
z2 = 0.04 =\frac{4}{100}
On taking square root on both sides, we get
\Rightarrow z= \pm \frac{2}{10}= \pm \frac{1}{5}
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 \pm \frac{1}{5} where 1, 5, -5 are rational numbers.
Hence z is rational.

(iv)Answer.          [Irrational]
Solution.        
Given that
u2 = \frac{17}{4}
On taking square root on both sides, we get
\Rightarrow u= \sqrt{\frac{17}{4}}= \pm \frac{\sqrt{17}}{2} 
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 \pm \frac{\sqrt{17}}{2} where \sqrt{17} is irrational.
Hence u is irrational.

 

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