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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.

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< sqrt56 <

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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality. $\newline$ $\square$ $\newline$ <\sqrt{56}< $\newline$ $\square$

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Simplify radical expressions with variables II

Full solution

Q. Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.

\newline

\square

\newline

<\sqrt{56}<

\newline

\square

Estimate square root: Step $1$ : Estimate the square root of $56$ by identifying perfect squares close to $56$ . The perfect squares close to $56$ are $49$ ( $7^2$ ) and $64$ ( $8^2$ ). Since $56$ is closer to $49$ , $\sqrt{56}$ is slightly more than $56$ $0$ but less than $56$ $1$ .
Determine integer range: Step $2$ : Determine the two consecutive integers between which $\sqrt{56}$ lies. $\newline$ Since $7^2 = 49$ and $8^2 = 64$ , and $56$ is between these two squares, $\sqrt{56}$ must be between $7$ and $8$ .

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