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

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2018-10-01T08:33:35+02:00

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

[tex]\sqrt(30)[/tex]

as

[tex]\sqrt(30)=\sqrt(2\times \times 3 \times 5)[/tex]

[tex]\Rightarrow \sqrt(30)=\sqrt(2 \times 3\times 5)[/tex]

[tex]\Rightarrow \sqrt(30)=\sqrt(2) \times \sqrt(3) \times \sqrt(5)[/tex]

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

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lublana lublana · Answer 2 · 2019-09-11T06:45:31+02:00

Answer:

Irrational number

Step-by-step explanation:

We are given that [tex]\sqrt{30}[/tex]

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

[tex]\sqrt{30}[/tex] can be written as

[tex]\sqrt{30}=\sqrt2\times \sqrt3\times \sqrt{5}[/tex]

We know that

[tex] \sqrt2, \sqrt3,\sqrt5[/tex] are irrational numbers .

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

Therefore, [tex]\sqrt{30}[/tex] is a irrational number.

Hence, [tex]\sqrt{30}[/tex] belongs to irrational number .