Question

Which of the following is true about the expression sqrt3*sqrt2

A.It represents the product of two irrational numbers and is equivalent to a rational number.
B.It represents the product of two irrational numbers and is equivalent to an irrational number.
C.It represents the product of two rational numbers and is equivalent to a rational number.
D.It represents the product of two rational numbers and is equivalent to an irrational number.

Answer 1

OPTION B

Explanation:

It represents the product of two irrational numbers and is equivalent to an irrational number.

Given:
`$ √(3) * √(2) $`.

These two numbers are irrational numbers.

Irrational numbers are those whose decimal representations either do not form a pattern or are non - terminating.

`$ √(2) = 1.414 \hdots $`

`$ √(3) = 1.732\hdots $`

They are irrational numbers.

Product of
`$ √(3) * √(2) $` =
`$ √(6) $`.

This is again an irrational number. So, OPTION B is the answer.

Answer 2

Option B is the right answer.

Explanation:

`√(3) , √(2)` are two irrational numbers, that is, they can not be shown as the fraction of two integers.

`√(3) *√(2) = √(6)`

`√(6)` is also a irrational number, since it also can not be represented as the fraction of integers.

Hence, the given expression represent the product of two irrational number and is equivalent to an irrational number.