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Which two integers is $\sqrt{103}$ between? $\newline$ Choices: $\newline$ (A) $8$ and $9$ $\newline$ (B) $9$ and $10$ $\newline$ (C) $12$ and $13$ $\newline$ (D) $10$ and $11$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

\sqrt{103}

between?

\newline

Choices:

\newline

(A)

8

and

9

\newline

(B)

9

and

10

\newline

(C)

12

and

13

\newline

(D)

10

and

11

Identify Perfect Squares: Identify the perfect squares close to $103$ . The perfect square just below $103$ is $100$ ( $10^2 = 100$ ). The perfect square just above $103$ is $121$ ( $11^2 = 121$ ).
Calculate Square Roots: Calculate the square roots of these perfect squares. $\newline$ $\sqrt{100} = 10$ $\newline$ $\sqrt{121} = 11$
Determine Integer Range: Determine between which two integers $\sqrt{103}$ falls. $\newline$ Since $100 < 103 < 121$ , then $10 < \sqrt{103} < 11$ .

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