Mathematics, 02.12.2019 04:31 kayliehernandez

Astudent memorized the statement the product of any rational number and an irrational number is irrational label this statement as true or false and explain your reasoning

Answers: 1

Show answers

Answers

A student memorized the statement the product of any rational number and an irrational number is irrational holds true for non-zero rational number

Solution:

A rational number is a number that can be written as a fraction.

When a rational number fraction is divided to form a decimal value,

it becomes a terminating or repeating decimal.

An Irrational Number is a real number that cannot be written as a simple fraction. It cannot be expressed as a fraction with integer values in the numerator and denominator.

When an irrational number is expressed in decimal form, it goes on forever without repeating.

"The product of a rational number and an irrational number is SOMETIMES irrational."

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.

Any other situation, however, of a product of rational and irrational will be irrational.

A better statement would be:

"The product of a non-zero rational number and an irrational number is irrational."

Let us understand this with a example

$\text { non - zero rational number } \times \text { irrational number }=\text { irrational number }$

Consider $\frac{1}{2} \rightarrow rational number$

$\frac{\sqrt{3}}{4} \rightarrow irrational number$

Now multiply both,

$\frac{1}{2} \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}=0.433012701$

We got 0.433012701 which is a irrational number because in decimal form, it goes on forever without repeating.

Thus we can frame two statements:

"The product of a rational number and an irrational number is SOMETIMES irrational." "The product of a non-zero rational number and an irrational number is irrational."

Answer from: lilquongohard

True.

Step-by-step explanation:

"The product of any rational number and an irrational number is irrational"

To know if the statement is true or false, we can test an example. Lets use the rational number $\frac{3}{2}$ and the irrational number $\pi$ . Id we calculate the product of these two we would have:

$\frac{3}{2}\pi= 4.71238898038469...$

As you can observe, the product is an irrational number, because it's infinite and not periodic, it doesn't have any pattern.

Therefore, the statement is true.

Answer from: Quest

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

Answer from: Quest

Ithink the answer is c

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Acoin bank containing only dimes and quarters has 12 more dimes than quarters. the total value of the coins is $11. how many quarters and dimes are in the coin bank?

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Amovie streaming service charges it’s customers $15 a month. martina has $98 saved up. will she have any money left over if she pays for the maximum amount of months she can afford? explain.

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Which expression is equal to (f+g)(x)?

Answers: 2

Answer

You know the right answer?

Astudent memorized the statement the product of any rational number and an irrational number is irra...

Questions