Question
What type of number will result from 512⋅16−−√ ?(1 point)
Responses
Radical, because one factor is a radical.
Radical, because one factor is a radical.
Irrational, because both factors are irrational.
Irrational, because both factors are irrational.
Rational, because both numbers are rational.
Rational, because both numbers are rational.
Irrational, because one factor is irrational.
Irrational, because one factor is irrational.
Responses
Radical, because one factor is a radical.
Radical, because one factor is a radical.
Irrational, because both factors are irrational.
Irrational, because both factors are irrational.
Rational, because both numbers are rational.
Rational, because both numbers are rational.
Irrational, because one factor is irrational.
Irrational, because one factor is irrational.
Answers
GPT-4o mini
To determine the type of number that results from \( 512 \cdot \sqrt{16} \), let’s break it down:
1. **Evaluate \(\sqrt{16}\)**:
\(\sqrt{16} = 4\), since \(4 \times 4 = 16\).
2. **Now, calculate \(512 \cdot 4\)**:
\(512 \cdot 4 = 2048\).
Next, let's evaluate the options given:
- **Radical, because one factor is a radical.** - **Incorrect**, since \(\sqrt{16}\) simplifies to a rational number (4).
- **Irrational, because both factors are irrational.** - **Incorrect**, since \(512\) (which is a whole number) and \(\sqrt{16}\) (which simplifies to 4) are both rational numbers.
- **Rational, because both numbers are rational.** - **Correct**, \(512\) is rational and \(4\) is rational, and the product \(2048\) is also rational.
- **Irrational, because one factor is irrational.** - **Incorrect**, as explained above.
Therefore, the correct response is:
**Rational, because both numbers are rational.**
1. **Evaluate \(\sqrt{16}\)**:
\(\sqrt{16} = 4\), since \(4 \times 4 = 16\).
2. **Now, calculate \(512 \cdot 4\)**:
\(512 \cdot 4 = 2048\).
Next, let's evaluate the options given:
- **Radical, because one factor is a radical.** - **Incorrect**, since \(\sqrt{16}\) simplifies to a rational number (4).
- **Irrational, because both factors are irrational.** - **Incorrect**, since \(512\) (which is a whole number) and \(\sqrt{16}\) (which simplifies to 4) are both rational numbers.
- **Rational, because both numbers are rational.** - **Correct**, \(512\) is rational and \(4\) is rational, and the product \(2048\) is also rational.
- **Irrational, because one factor is irrational.** - **Incorrect**, as explained above.
Therefore, the correct response is:
**Rational, because both numbers are rational.**