Answer:
[tex]b.\sqrt{\frac{2}{4}}[/tex]
c.[tex]\sqrt{\frac{3}{4}}[/tex]
[tex]e.\sqrt{\frac{5}{4}}[/tex]
Step-by-step explanation:
Rational number: The number which can be written as [tex]\frac{p}{q}[/tex] , where p and q are integers,[tex]q\neq 0[/tex]
Irrational number: When the number is not rational number then, the number is called irrational number.
We have to find the irrational numbers.
a.[tex]\sqrt{\frac{1}{4}}[/tex]
We can write as
[tex]\frac{1}{2}[/tex]
Because [tex]\sqrt{4}=2[/tex]
[tex]\frac{1}{2}[/tex] is a rational number because 1 and 2 are both integers and [tex]2\neq 0[/tex]
Hence, a is not true.
b.[tex]\sqrt{\frac{2}{4}}[/tex]
[tex]\frac{1}{\sqrt2}[/tex]
We know that [tex]\sqrt2[/tex] is irrational number.
When a rational number is divided by irrational number then we get a irrational number.
[tex]\frac{1}{\sqrt2}[/tex] is irrational number.
c.[tex]\sqrt{\frac{3}{4}}[/tex]
[tex]\frac{\sqrt3}{2}[/tex]
We know that
[tex]\sqrt3[/tex] is irrational number.Therefore,
[tex]\frac{\sqrt3}{2}[/tex] is irrational number.
Hence, option c is true.
d.[tex]\sqrt{\frac{4}{4}}[/tex]
[tex]\sqrt1[/tex]
[tex]\sqrt1=1[/tex]
1 is rational number.
Hence, option d is false.
e.[tex]\sqrt{\frac{5}{4}}[/tex]
[tex]\frac{\sqrt5}{2}[/tex]
We know that [tex]\sqrt5[/tex] is irrational number
Therefore, [tex]\frac{\sqrt5}{2}[/tex] is irrational number.
Hence, option e is true.
