Which number is closest to sqrt 37 ? Choices: (A)5.8 (B)6.0 (C)5.6 (D)6.9

Identify Perfect Squares: Step 1: Identify the perfect squares closest to 37 to estimate the square root. Since 36 (6^2) is less than 37 and 49 (7^2) is more than 37, the square root of 37 must be between 6 and 7.Compare Given Choices: Step 2: Compare the given choices to our estimated range. Choices are (A) 5.8, (B) 6.0, (C) 5.6, (D) 6.9. Since we know the square root of 37 is between 6 and 7, we can eliminate choices (A) and (C).Calculate Square of Choices: Step 3: Calculate the square of the remaining choices to see which is closer to 37. 6.0^2 = 36 6.9^2 = 47.61 Since 36 is closer to 37 than 47.61, choice (B) 6.0 is closer to the square root of 37.

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Which number is closest to $\sqrt{37}$ ? $\newline$ Choices: $\newline$ (A) $5.8$ $\newline$ (B) $6.0$ $\newline$ (C) $5.6$ $\newline$ (D) $6.9$

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Math Problems

Grade 7

Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{37}

\newline

Choices:

\newline

(A)

5.8

\newline

(B)

6.0

\newline

(C)

5.6

\newline

(D)

6.9

Identify Perfect Squares: Step $1$ : Identify the perfect squares closest to $37$ to estimate the square root. $\newline$ Since $36$ ( $6^2$ ) is less than $37$ and $49$ ( $7^2$ ) is more than $37$ , the square root of $37$ must be between $6$ and $7$ .
Compare Given Choices: Step $2$ : Compare the given choices to our estimated range. Choices are $(A) 5.8, (B) 6.0, (C) 5.6, (D) 6.9$ . Since we know the square root of $37$ is between $6$ and $7$ , we can eliminate choices $(A)$ and $(C)$ .
Calculate Square of Choices: Step $3$ : Calculate the square of the remaining choices to see which is closer to $37$ . $\newline$ $6.0^2 = 36$ $\newline$ $6.9^2 = 47.61$ $\newline$ Since $36$ is closer to $37$ than $47.61$ , choice (B) $6.0$ is closer to the square root of $37$ .