The product of 100−−−√

Question

and 415
will be what type of number?(1 point)
Responses

irrational
irrational - no response given

zero
zero - no response given

an integer
an integer - incorrect

rational
rational - no response given
Incorrect

Will the product of rational numbers always be an integer?
Remaining Attempts : 2

Answer 1

To determine the product of \(\sqrt{100}\) and \(415\):

1. Calculate \(\sqrt{100}\): \[ \sqrt{100} = 10 \]

2. Now, multiply \(10\) by \(415\): \[ 10 \times 415 = 4150 \]

So, the product of \(\sqrt{100}\) and \(415\) is \(4150\), which is an integer.

Regarding your second question, Will the product of rational numbers always be an integer?

The answer is no. The product of rational numbers is not always an integer; it will be a rational number. For example, multiplying \(\frac{1}{2}\) and \(\frac{1}{3}\) gives \(\frac{1}{6}\), which is a rational number but not an integer.

Summary:

• The product of \(\sqrt{100}\) and \(415\) is \(4150\), which is an integer.
• The product of rational numbers is always a rational number, but not necessarily an integer.