Question

Find the answer to zero point 73 repeating times square root of 147 end square root and select the correct answer below. Also, is the product of a nonzero rational number and an irrational number classified as rational or irrational? start fraction 80 over 99 end fraction square root of three end square root comma rational start fraction 511 over 99 end fraction square root of three end square root comma irrational 511 over 33, rational start fraction 73 over 99 end fraction plus seven square root of three end square root comma irrational

Answer 1

`(511\,\,√(3) )/(99)` which is an irrational number

Explanation:

Recall that the repeating decimal 0.7373737373... can be written in fraction form as:
`(73)/(99)`

Now, let's write the number 147 which is inside the square root in factor form to find if it has some perfect square factors:

`147=7^2\,3`

Then, 7 will be able to go outside the root when we compute the final product requested:

`(73)/(99) \,*\,7\,√(3) =(511\,\,√(3) )/(99)`

This is an irrational number due to the fact that it is the product of a rational number (quotient between 511 and 99) times the irrational number
`√(3)`