Question

state whether the following numbers are rational or not: 1) 5√3×√12​

Answer 1

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