Which of the following is closest to the approximate value of the square root of 2400?

Which of the following is closest to the approximate value of the square root of 2400?

• A. 48.99
• B. 49.00
• C. 49.01
• D. 49.02

Answer: (B)

To estimate the square root of 2400, we can begin by breaking it down into its prime factors. The number 2400 can be expressed as \( 2400 = 24 \times 100 \) or further factored as \( 2400 = 24 \times 10^2 \). To simplify our calculations, we find the square root of 100, which is straightforward at 10. Next, we focus on calculating the square root of 24. Noting that \( 24 = 4 \times 6 \), we can find that \( \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \). The value of \( \sqrt{6} \) is approximately 2.45, leading us to approximate \( \sqrt{24} \approx 2 \times 2.45 = 4.9 \). Thus, we can calculate \( \sqrt{2400} \) as follows: \[ \sqrt{2400} = \sqrt{24 \times 100} = \sqrt{24} \times \sqrt{100}

To estimate the square root of 2400, we can begin by breaking it down into its prime factors. The number 2400 can be expressed as ( 2400 = 24 \times 100 ) or further factored as ( 2400 = 24 \times 10^2 ).

To simplify our calculations, we find the square root of 100, which is straightforward at 10. Next, we focus on calculating the square root of 24. Noting that ( 24 = 4 \times 6 ), we can find that ( \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} ).

The value of ( \sqrt{6} ) is approximately 2.45, leading us to approximate ( \sqrt{24} \approx 2 \times 2.45 = 4.9 ). Thus, we can calculate ( \sqrt{2400} ) as follows:

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\sqrt{2400} = \sqrt{24 \times 100} = \sqrt{24} \times \sqrt{100}