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The value of square root of 7 is between 2 and 3. Which of the following is a more precise approximation of square root of 7?

A.
between 2.6 and 2.7
B.
between 2.7 and 2.8
C.
between 2.8 and 2.9
D.
between 2.4 and 2.5

5 answers

To determine a more precise approximation for \(\sqrt{7}\), we can calculate the squares of the numbers within the given ranges.

  1. For option A (between 2.6 and 2.7):

    • \(2.6^2 = 6.76\)
    • \(2.7^2 = 7.29\)

    Since \(6.76 < 7 < 7.29\), this range is valid.

  2. For option B (between 2.7 and 2.8):

    • \(2.7^2 = 7.29\)
    • \(2.8^2 = 7.84\)

    Since \(7 < 7.29\), this range is not valid.

  3. For option C (between 2.8 and 2.9):

    • \(2.8^2 = 7.84\)
    • \(2.9^2 = 8.41\)

    Since \(7 < 7.84\), this range is also not valid.

  4. For option D (between 2.4 and 2.5):

    • \(2.4^2 = 5.76\)
    • \(2.5^2 = 6.25\)

    Since \(7 > 6.25\), this range is not valid.

Based on our calculations, the only valid range for \(\sqrt{7}\) is option A: between 2.6 and 2.7.

Thus, the most precise approximation of \(\sqrt{7}\) is:

A. between 2.6 and 2.7.

Select the correct answer from the drop-down menu.
Complete the statement by choosing the symbol that correctly compares the number

–5 Pi ___ – square root of 45

A. =

B. <

C. >

To compare \(-5\pi\) and \(-\sqrt{45}\), we first need to calculate the approximate values of these expressions.

  1. Calculate \(-5\pi\):

    • Using \(\pi \approx 3.14\), we find: \[ -5\pi \approx -5 \times 3.14 \approx -15.7 \]

  2. Calculate \(-\sqrt{45}\):

    • First find \(\sqrt{45}\): \[ \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \]
    • Approximating \(\sqrt{5} \approx 2.24\): \[ \sqrt{45} \approx 3 \times 2.24 \approx 6.72 \]
    • Thus: \[ -\sqrt{45} \approx -6.72 \]

Now we compare the two results:

  • \(-5\pi \approx -15.7\)
  • \(-\sqrt{45} \approx -6.72\)

Since \(-15.7\) is less than \(-6.72\), we can conclude that:

\(-5\pi < -\sqrt{45}\).

Therefore, the correct answer to complete the statement is:

B. <

Determine which two values the following expression is between.
2 square roof of 5

A.
4.46 and 4.47
B.
4.44 and 4.45
C.
4.45 and 4.46
D.
4.47 and 4.48

To determine which two values \(2 \sqrt{5}\) is between, we first calculate the value of \(\sqrt{5}\).

  1. Calculate \(\sqrt{5}\):

    • We know that \(\sqrt{5} \approx 2.236\).

  2. Now calculate \(2 \sqrt{5}\): \[ 2 \sqrt{5} \approx 2 \times 2.236 = 4.472 \]

Now, let's examine the options provided and see which two values \(4.472\) falls between:

  • A. 4.46 and 4.47: \(4.46 < 4.472 < 4.47\) (True)
  • B. 4.44 and 4.45: \(4.44 < 4.472 < 4.45\) (False)
  • C. 4.45 and 4.46: \(4.45 < 4.472 < 4.46\) (False)
  • D. 4.47 and 4.48: \(4.47 < 4.472 < 4.48\) (True)

The correct intervals that contain \(2 \sqrt{5} \approx 4.472\) are given by options A and D:

  • Option A: 4.46 and 4.47
  • Option D: 4.47 and 4.48

Since \(4.472\) is specifically between \(4.46\) and \(4.47\), the more precise interval for \(2 \sqrt{5}\) is:

A. 4.46 and 4.47.