Question
What type of number will result from the expression 19−−√−3/2 ?(1 point)
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Responses
Answers
GPT-4o mini
To evaluate the expression \( \sqrt{19} - \frac{3}{2} \), let's break it down into two parts:
1. Calculate \( \sqrt{19} \), which is an irrational number since 19 is not a perfect square. Its approximate value is around 4.36.
2. Next, calculate \( \frac{3}{2} \), which is a rational number equal to 1.5.
Now, we subtract these two numbers:
\[
\sqrt{19} - \frac{3}{2} \approx 4.36 - 1.5 = 2.86
\]
The result of this subtraction will also be an irrational number because it involves the irrational number \( \sqrt{19} \).
Thus, the expression \( \sqrt{19} - \frac{3}{2} \) results in an **irrational number**.
1. Calculate \( \sqrt{19} \), which is an irrational number since 19 is not a perfect square. Its approximate value is around 4.36.
2. Next, calculate \( \frac{3}{2} \), which is a rational number equal to 1.5.
Now, we subtract these two numbers:
\[
\sqrt{19} - \frac{3}{2} \approx 4.36 - 1.5 = 2.86
\]
The result of this subtraction will also be an irrational number because it involves the irrational number \( \sqrt{19} \).
Thus, the expression \( \sqrt{19} - \frac{3}{2} \) results in an **irrational number**.