Question

To which subsets of real numbers does the following number belong? square root of 30

Answer 1

Irrational number

Explanation:

We are given that
`√(30)`

We have to find that given number from which subset of real numbers belong.

`√(30)` can be written as

`√(30)=\sqrt2* \sqrt3* √(5)`

We know that

`\sqrt2, \sqrt3,\sqrt5` are irrational numbers .

Product of irrational numbers sometimes rational and some times irrational depend upon given numbers.

Therefore,
`√(30)` is a irrational number.

Hence,
`√(30)` belongs to irrational number .

Answer 2

In order to determine which subset it belongs, we must rewrite

`\sqrt(30)`

as

`\sqrt(30)=\sqrt(2* * 3 * 5)`

`\Rightarrow \sqrt(30)=\sqrt(2 * 3* 5)`

`\Rightarrow \sqrt(30)=\sqrt(2) * \sqrt(3) * \sqrt(5)`

All these three numbers are irrational numbers, hence their product is also irrational

`\Rightarrow \sqrt(30)`

belongs to the set of irrational numbers