Question
what type of number will result from the expression sqaure root 19 -3/2?
Answers
Answered by
GPT-4o mini
To evaluate the expression \(\sqrt{19} - \frac{3}{2}\), we start by calculating each part:
1. **Calculate \(\sqrt{19}\)**: The square root of 19 is approximately 4.3589 (a non-repeating, non-terminating decimal).
2. **Subtract \(\frac{3}{2}\)**: Since \(\frac{3}{2} = 1.5\), we can rewrite the expression as:
\[
4.3589 - 1.5 = 2.8589
\]
The result of \(\sqrt{19} - \frac{3}{2}\) is therefore approximately 2.8589.
In terms of number types:
- The square root of 19 is an irrational number (since 19 is not a perfect square).
- The fraction \(\frac{3}{2}\) is a rational number.
- Their difference \(\sqrt{19} - \frac{3}{2}\) is also an irrational number since the subtraction of a rational number from an irrational number yields an irrational number.
Thus, the result of the expression \(\sqrt{19} - \frac{3}{2}\) is an **irrational number**.
1. **Calculate \(\sqrt{19}\)**: The square root of 19 is approximately 4.3589 (a non-repeating, non-terminating decimal).
2. **Subtract \(\frac{3}{2}\)**: Since \(\frac{3}{2} = 1.5\), we can rewrite the expression as:
\[
4.3589 - 1.5 = 2.8589
\]
The result of \(\sqrt{19} - \frac{3}{2}\) is therefore approximately 2.8589.
In terms of number types:
- The square root of 19 is an irrational number (since 19 is not a perfect square).
- The fraction \(\frac{3}{2}\) is a rational number.
- Their difference \(\sqrt{19} - \frac{3}{2}\) is also an irrational number since the subtraction of a rational number from an irrational number yields an irrational number.
Thus, the result of the expression \(\sqrt{19} - \frac{3}{2}\) is an **irrational number**.