Find the square root of 96. A. 16
6
B. 6
4
C. 24 D. 4
6
The Correct Answer and Explanation is :
To find the square root of 96, we first need to express 96 in a simpler form. The square root of a number is a value that, when multiplied by itself, gives the original number. We can simplify the square root by factoring 96.
- Factoring 96: We start by finding the prime factors of 96.
- Divide by 2: (96 \div 2 = 48)
- Divide by 2 again: (48 \div 2 = 24)
- Divide by 2 again: (24 \div 2 = 12)
- Divide by 2 again: (12 \div 2 = 6)
- Divide by 2 again: (6 \div 2 = 3)
- Finally, 3 is a prime number. Thus, the prime factorization of 96 is (2^5 \times 3).
- Taking the Square Root:
To find the square root of 96, we can apply the square root to the prime factorization:
[
\sqrt{96} = \sqrt{2^5 \times 3} = \sqrt{(2^4 \times 2) \times 3} = \sqrt{2^4} \times \sqrt{2} \times \sqrt{3}
]
Knowing that (\sqrt{2^4} = 2^2 = 4), we can further simplify:
[
\sqrt{96} = 4 \times \sqrt{6}
] - Approximation: To get a numerical approximation, we need the value of (\sqrt{6}). It is approximately 2.449. Therefore:
[
4 \times \sqrt{6} \approx 4 \times 2.449 \approx 9.796
]
This indicates that the square root of 96 is about 9.8.
Based on the options provided:
- A. (16 \sqrt{6})
- B. (6 \sqrt{4}) (which equals 12)
- C. (24)
- D. (4 \sqrt{6})
The correct answer is D. (4 \sqrt{6}), as it is the only option that accurately represents the square root of 96 in simplified radical form.