High School

Without using a calculator, order the following expressions from least to greatest:

7.12
[tex]\sqrt{75}[/tex]
145

A. 7.12; [tex]\sqrt{75}[/tex]; 145
B. [tex]\sqrt{75}[/tex]; 145; 7.12
C. 145; 7.12; [tex]\sqrt{75}[/tex]
D. None of the above

Answer :

Final answer:

The correct order of the given expressions from least to greatest is: √75, 7.12, 145.

Explanation:

The correct order of the given expressions from least to greatest is:

  1. √75
  2. 7.12
  3. 145

We can determine the order of these expressions without using a calculator by comparing their values. The square root of 75 (√75) is approximately 8.66, which is less than 7.12. Hence, √75 comes first. Next, we have 7.12 which comes before 145. Therefore, the correct order is √75, 7.12, 145. Consequently, this methodical evaluation reveals the order of the given expressions, showcasing their hierarchical arrangement based on their respective values without the need for precise calculations.

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