Question

Which set(s) of numbers does the 20−−√20 belong to? (click all that apply)

Natural Number

Whole Number

Integer

Rational numbers

Irrational Number
please help me

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Answer 1

Given : The number is
`√(20)`.

To find: Set(s) of numbers in which
`√(20)` belong to.

Solution:

We know that,

Natural Number
`=\{1,2,3,...\}`

Whole Number
`=\{0,1,2,3,...\}`

Integer
`=\{...-3,-2,-1,0,1,2,3,...\}`

Rational numbers
`=\{-2,0,3.4,(1)/(2)\text{ etc}\}`

Irrational numbers
`=\{√(2),√(3),\pi, 1.25436...\text{ etc}\}`

We have,

`√(20)=√(4* 5)`

`√(20)=√(4)* √(5)`

`√(20)=2* √(5)`

`√(20)=2√(5)`

So,
`√(20)` is the product of a non zero rational number, i.e., 2 and an irrational number, i.e.,
`√(5)`.

We know that product of a non zero rational number and an irrational number is always irrational.

So,
`√(20)` is an irrational number.

Therefore, the correct option is 5.