Question

What type of number will result from 5/12 x the square root of 16?

A: Radical, because one factor is a radical

B: irrational because one factor is irrational

C: Rational because both numbers are rational

D: irrational , because both factors are irrational

Answer 1

Let's evaluate the expression \( \frac{5}{12} \times \sqrt{16} \).

1. Calculate \( \sqrt{16} \):
\[
\sqrt{16} = 4
\]

2. Now substitute back into the expression:
\[
\frac{5}{12} \times 4
\]

3. Multiply \( 4 \) by \( \frac{5}{12} \):
\[
\frac{5 \times 4}{12} = \frac{20}{12}
\]

4. Simplify \( \frac{20}{12} \):
\[
\frac{20}{12} = \frac{5}{3} \quad (\text{after dividing numerator and denominator by } 4)
\]

Since \( \frac{5}{3} \) is a rational number, the answer is:

**C: Rational because both numbers are rational**.