Question

Select all irrational numbers.

a.) √1/4
b.) √2/4
c.) √3/4
d.) √4/4
e.) √5/4

Note: these are all the square root of FRACTIONS they are not being divided!!!

Answer 1

Rational: a.) and d.)
Irrational: b.), c.), and e.)

Answer 2

`b.\sqrt{(2)/(4)}`

c.
`\sqrt{(3)/(4)}`

`e.\sqrt{(5)/(4)}`

Explanation:

Rational number: The number which can be written as
`(p)/(q)` , where p and q are integers,
`q\\eq 0`

Irrational number: When the number is not rational number then, the number is called irrational number.

We have to find the irrational numbers.

a.
`\sqrt{(1)/(4)}`

We can write as

`(1)/(2)`

Because
`√(4)=2`

`(1)/(2)` is a rational number because 1 and 2 are both integers and
`2\\eq 0`

Hence, a is not true.

b.
`\sqrt{(2)/(4)}`

`(1)/(\sqrt2)`

We know that
`\sqrt2` is irrational number.

When a rational number is divided by irrational number then we get a irrational number.

`(1)/(\sqrt2)` is irrational number.

c.
`\sqrt{(3)/(4)}`

`(\sqrt3)/(2)`

We know that

`\sqrt3` is irrational number.Therefore,

`(\sqrt3)/(2)` is irrational number.

Hence, option c is true.

d.
`\sqrt{(4)/(4)}`

`\sqrt1`

`\sqrt1=1`

1 is rational number.

Hence, option d is false.

e.
`\sqrt{(5)/(4)}`

`(\sqrt5)/(2)`

We know that
`\sqrt5` is irrational number

Therefore,
`(\sqrt5)/(2)` is irrational number.

Hence, option e is true.