state whether the following numbers are rational or not: 1) 5√3×√12
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Answer :-
Yes.
The given number is a rational number.
Step-by-step explanation :-
This is because:
√12 can be written as √(4 × 3) = √4 × √3 = 2√3
Here,
5√3 is multiplied with √12.
This also implies that:
5√3 is multiplied with 2√3
⇒ 5√3 × 2√3
⇒ 5 × 2 × √3 × √3
⇒ 10 × 3
⇒ 30
Definitely 30 is a rational number.
So, the given number is a rational number.
KNOW MORE:
- When 2 irrational numbers of the same base are multiplied, then the resulting number would be a rational number.
Example: √2 × √2 = 2
- When 2 irrational numbers of different bases are multiplied, then the resulting number would either be rational or irrational
Example:
★ √2 × √3 = √6
★ √32 × √2 = √64 = 8
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