What type of number will result from 5/12⋅√16 ?(1 point)

Question

Responses

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Irrational, because one factor is irrational.
Irrational, because one factor is irrational.

Radical, because one factor is a radical.
Radical, because one factor is a radical.

Irrational, because both factors are irrational.

Answer 1

To determine the type of number that results from \( \frac{5}{12} \cdot \sqrt{16} \), we can first simplify the expression.

1. First, we compute \( \sqrt{16} \): \[ \sqrt{16} = 4 \]

2. Now, we substitute \( 4 \) back into the expression: \[ \frac{5}{12} \cdot 4 \]

3. Next, we multiply: \[ \frac{5 \cdot 4}{12} = \frac{20}{12} \]

4. We can simplify \( \frac{20}{12} \): \[ \frac{20}{12} = \frac{5}{3} \]

Since \( \frac{5}{3} \) is a fraction of two integers, it is a rational number.

Thus, the correct response is: Rational, because both numbers are rational.

Answer 2

r u sure-sure?

Answer 3

Yes, I am sure!

Let's recap the reasoning:

1. Calculate \(\sqrt{16}\): This yields \(4\), which is a rational number.
2. Multiply \(\frac{5}{12}\) by \(4\): This gives \(\frac{5 \times 4}{12} = \frac{20}{12}\).
3. Simplify \(\frac{20}{12}\): This reduces to \(\frac{5}{3}\), which is also a rational number.

Since both the original numbers (\(\frac{5}{12}\) and \(4\)) are rational, their product will also be rational. Therefore, the final answer is indeed Rational, because both numbers are rational.