Which number is closest to sqrt 82 ? Choices: (A)10.3 (B)10.2 (C)9.0 (D)9.7

Identify Perfect Square: Step 1: Identify the square root of a perfect square close to 82 for estimation. Since 81 is a perfect square (9^2 = 81), and 100 is the next perfect square (10^2 = 100), sqrt(82) will be slightly more than 9 but less than 10.Calculate Square Root: Step 2: Calculate the square root of 82 using a calculator for more accuracy. sqrt(82) ≈ 9.0554Compare with Choices: Step 3: Compare the calculated square root with the given choices. - 10.3 is too high. - 10.2 is also too high. - 9.0 is close, but let's check 9.7. - 9.7 is closer to 9.0554 than 9.0.

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Which number is closest to $\sqrt{82}$ ? $\newline$ Choices: $\newline$ (A) $10.3$ $\newline$ (B) $10.2$ $\newline$ (C) $9.0$ $\newline$ (D) $9.7$

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Math Problems

Grade 7

Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{82}

\newline

Choices:

\newline

(A)

10.3

\newline

(B)

10.2

\newline

(C)

9.0

\newline

(D)

9.7

Identify Perfect Square: Step $1$ : Identify the square root of a perfect square close to $82$ for estimation. $\newline$ Since $81$ is a perfect square ( $9^2 = 81$ ), and $100$ is the next perfect square ( $10^2 = 100$ ), $\sqrt{82}$ will be slightly more than $9$ but less than $10$ .
Calculate Square Root: Step ext{ $2$ }: Calculate the square root of ext{ $82$ } using a calculator for more accuracy. $\newline$ $\sqrt{82} \approx 9.0554$
Compare with Choices: Step $3$ : Compare the calculated square root with the given choices. $\newline$ - $10.3$ is too high. $\newline$ - $10.2$ is also too high. $\newline$ - $9.0$ is close, but let's check $9.7$ . $\newline$ - $9.7$ is closer to $9.0554$ than $9.0$ .