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Q: Can you multiply an irrational number times an irrational number and get a rational number?

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No; since pi is irrational if you multiply it by a rational number it is still irrational

No. If the rational number is not zero, then such a product is irrational.

No.A rational times an irrational is never rational. It is always irrational.

Unless the rational number is zero, the answer is irrational.

Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]

Not necessarily. 0 times any irrational number is 0 - which is rational.

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)

The square root of 2 times the square root of 2 is rational.

At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.

75 times 75 = 5625 which is a rational number

There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.

It the radius is r then the area is pi*r*r - which is pi times a rational number. pi is an irrational number, so the multiple of pi and a rational number is irrational.

No because 15 times pi is an irrational number

Any number times pi is irrational.

3 times pi is an irrational number because it can't be expressed as a fraction

It is not. It is the rational number 6.28 = 628/100.

If you mean 0.3 times pi then it is an irrational number

As the area of a rectangle is one side (length) multiples by the other (width), if either is irrational, then the area will be irrational. eg a rectangle with width 1 cm and diagonal 2 cm: using Pythagoras you can find out the length of the rectangle as √(2² - 1²) = √(4 - 1) = √3 which is irrational. The area of the rectangle is 1 cm × √3 cm = √3 cm² (which is irrational).

Not always. For example sqrt(2) and 1/sqrt(2) are both irrational, but their product is the rational number 1.

No because the value of pi as regards to a circle is an irrational number

A decimal, in this context, is a useless description: a decimal can be an integer, a rational number or an irrational number. Furthermore, a whole number times a decimal fraction can be a whole number, a rational number or an irrational number.For example:4 * 3.5 = 14 is a whole number times a decimal fraction = whole number.4 * 3.3 = 13.2 is a whole number times a decimal fraction = rational fraction.4 * 3.14159... [ie pi in decimal form] = 4 * pi, which is an irrational number.

No because it is 2 times the square root of 21 which is an irrational numberThe square root of 84 is not a rational number

I assume you mean 2 times pi. Since pi is irrational, 2 pi is also irrational.

yes it can, look at the example √3 times the √3 is 3. these two are rational numbers.