SOLUTION: How do i detemrine whether the product of an irrational number times a rational number is a rational or irrational? for example 3X square root of 11

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Question 1088311: How do i detemrine whether the product of an irrational number times a rational number is a rational or irrational?
for example 3X square root of 11 - irrational or rational?

Found 3 solutions by natolino_2017, MathTherapy, ikleyn:
Answer by natolino_2017(77)   (Show Source):
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you need to convert the rational number into a expression similary to the irrational number.
In the example 3 = sqrt(9).
so 3*sqrt(11) = sqrt(9)*sqrt(99) = sqrt(99) which is an irrational number

Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!

How do i detemrine whether the product of an irrational number times a rational number is a rational or irrational?
for example 3X square root of 11 - irrational or rational?

If this is , then that's the PRODUCT of a RATIONAL and an IRRATIONAL number, which results in a number that's

Answer by ikleyn(52884)   (Show Source):
You can put this solution on YOUR website!
.
The product of an irrational number times a rational number (except ZERO) is ALWAYS irrational number.

SOLUTION: How do i detemrine whether the product of an irrational number times a rational number is a rational or irrational? for example 3X square root of 11 - irrational or rational?