Question

I am offering another 100 points

Answer 1

Answer:8 and 9, since square root of 64 is 8 and square root of 81 is 9, it is known that square root of 75 is between 8 and 9

Explanation:

Answer 2

`\sf Since \;\sqrt{\boxed{64}}=\boxed{8}\;and\;\sqrt{\boxed{81}}=\boxed{9}\; \textsf{it is known that $√(75)$ is between}\\\\\sf \boxed{8}\;and\;\boxed{9}\;.`

Explanation:

Perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...

To find
`\sf √(75)` , identify the perfect squares immediately before and after 75:

• 64 and 81

`\begin{aligned}\sf As\;\; 64 < 75 < 81\; & \implies \sf √(64) < √(75) < √(81)\\&\implies \sf \;\;\;\;\;8 < √(75) < 9 \end{aligned}`

`\sf Since \;\sqrt{\boxed{64}}=\boxed{8}\;and\;\sqrt{\boxed{81}}=\boxed{9}\; \textsf{it is known that $√(75)$ is between}\\\\\sf \boxed{8}\;and\;\boxed{9}\;.`

See the attachment for the correct placement of
`\sf √(75)` on the number line.