Pregunta
Which square root is between 4 and 5 ? \( \sqrt{10} \) \( \sqrt{14} \) \( \sqrt{24} \) \( \sqrt{32} \)
Ask by Newton Byrd. in the United States
Mar 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( \sqrt{24} \) is between 4 and 5.
Solución
1. Recognize that for a square root \( \sqrt{x} \) to be between 4 and 5, the radicand \( x \) must satisfy
\[
4^2 < x < 5^2,
\]
which simplifies to
\[
16 < x < 25.
\]
2. Check each option:
- For \( \sqrt{10} \): \( 10 \) is less than 16.
- For \( \sqrt{14} \): \( 14 \) is less than 16.
- For \( \sqrt{24} \): \( 24 \) is between 16 and 25.
- For \( \sqrt{32} \): \( 32 \) is greater than 25.
3. Since only \( 24 \) satisfies \( 16 < x < 25 \), the square root between 4 and 5 is
\[
\sqrt{24}.
\]
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Simplifique esta solución Extra Insights
Did you know that the square root of a number is essentially finding a value that, when multiplied by itself, equals that number? In this case, \( \sqrt{10} \) is approximately 3.16, \( \sqrt{14} \) is around 3.74, \( \sqrt{24} \) is about 4.89, and \( \sqrt{32} \) lands roughly at 5.66. So, \( \sqrt{24} \) is the only one nestled right between 4 and 5! If you’re ever unsure which square root fits your desired range, a quick way to estimate is by squaring your bounds! For example, since \(4^2 = 16\) and \(5^2 = 25\), you can check which square roots fall between 16 and 25. This helps in narrowing down where to look!
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