Question

Which of the following values for m makes the inequality m−−√+17<24
true?
49
49

48
48

50
50

64

Answer 1

To solve the inequality \( \sqrt{m} + 17 < 24 \), we will first isolate \( \sqrt{m} \).

1. Subtract 17 from both sides:

\[
\sqrt{m} < 24 - 17
\]

This simplifies to:

\[
\sqrt{m} < 7
\]

2. Next, we square both sides to eliminate the square root (keeping in mind that squaring both sides is valid since both sides are positive):

\[
m < 7^2
\]

This gives us:

\[
m < 49
\]

Now, we will test the given values:

1. **For \( m = 49 \)**:
\[
\sqrt{49} + 17 = 7 + 17 = 24 \quad \text{(not less than 24)}
\]

2. **For \( m = 48 \)**:
\[
\sqrt{48} + 17 \approx 6.93 + 17 \approx 23.93 < 24 \quad \text{(true)}
\]

3. **For \( m = 50 \)**:
\[
\sqrt{50} + 17 \approx 7.07 + 17 \approx 24.07 \quad \text{(not less than 24)}
\]

4. **For \( m = 64 \)**:
\[
\sqrt{64} + 17 = 8 + 17 = 25 \quad \text{(not less than 24)}
\]

Based on the tests, the only value for \( m \) that makes the inequality \( \sqrt{m} + 17 < 24 \) true is:

\[
\boxed{48}
\]