Question
What type of number will result from the expression square root of 19 minus 3/2 but is it a rational number, irrational, whole number, or an integar
Answers
GPT-4o mini
To determine the type of number that results from the expression \(\sqrt{19} - \frac{3}{2}\), we can analyze each part:
1. **Evaluate \(\sqrt{19}\)**: The square root of 19 is an irrational number because 19 is not a perfect square.
2. **Evaluate \(\frac{3}{2}\)**: This is a rational number since it can be expressed as the fraction of two integers.
Now we consider the expression:
\[
\sqrt{19} - \frac{3}{2}
\]
Since \(\sqrt{19}\) is irrational and \(\frac{3}{2}\) is rational, the result of subtracting a rational number from an irrational number is still irrational.
Thus, \(\sqrt{19} - \frac{3}{2}\) is an **irrational number**.
1. **Evaluate \(\sqrt{19}\)**: The square root of 19 is an irrational number because 19 is not a perfect square.
2. **Evaluate \(\frac{3}{2}\)**: This is a rational number since it can be expressed as the fraction of two integers.
Now we consider the expression:
\[
\sqrt{19} - \frac{3}{2}
\]
Since \(\sqrt{19}\) is irrational and \(\frac{3}{2}\) is rational, the result of subtracting a rational number from an irrational number is still irrational.
Thus, \(\sqrt{19} - \frac{3}{2}\) is an **irrational number**.