Which number is closest to sqrt 23 ? Choices: (A)4.7 (B)4.4 (C)5.5 (D)3.6

Understand the problem: Step 1: Understand the problem. We need to find which number among the choices is closest to the square root of 23. Estimate square root: Step 2: Estimate the square root of 23. Since 23 is between the squares of 4 (16) and 5 (25), its square root must be between 4 and 5. Calculate square root: Step 3: Calculate the square root of 23 using a calculator for more accuracy. sqrt(23) ≈ 4.7958. Compare with choices: Step 4: Compare the calculated square root with the given choices. - Difference with 4.7 is |4.7958 - 4.7| = 0.0958 - Difference with 4.4 is |4.7958 - 4.4| = 0.3958 - Difference with 5.5 is |4.7958 - 5.5| = 0.7042 - Difference with 3.6 is |4.7958 - 3.6| = 1.1958Determine closest value: Step 5: Determine the closest value. The smallest difference is with 4.7, so 4.7 is the closest to the square root of 23.

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Math Problems

Grade 7

Estimate square roots

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Q. Which number is closest to

\sqrt{23}

\newline

Choices:

\newline

(A)

4.7

\newline

(B)

4.4

\newline

(C)

5.5

\newline

(D)

3.6

Understand the problem: Step $1$ : Understand the problem. We need to find which number among the choices is closest to the square root of $23$ .
Estimate square root: Step $2$ : Estimate the square root of $23$ . Since $23$ is between the squares of $4$ ( $16$ ) and $5$ ( $25$ ), its square root must be between $4$ and $5$ .
Calculate square root: Step $3$ : Calculate the square root of $23$ using a calculator for more accuracy. $\sqrt{23} \approx 4.7958$ .
Compare with choices: Step $4$ : Compare the calculated square root with the given choices. $\newline$ - Difference with $4.7$ is $|4.7958 - 4.7| = 0.0958$ $\newline$ - Difference with $4.4$ is $|4.7958 - 4.4| = 0.3958$ $\newline$ - Difference with $5.5$ is $|4.7958 - 5.5| = 0.7042$ $\newline$ - Difference with $3.6$ is $|4.7958 - 3.6| = 1.1958$
Determine closest value: Step $5$ : Determine the closest value. The smallest difference is with $4.7$ , so $4.7$ is the closest to the square root of $23$ .