Question

Which of the
following numbers
falls between 8 and 9
on the number line
square root of 75 or square root of 100?

Answer 1

Answer:  $\sqrt{75}$

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Explanation:

Square both 8 and 9 to get

• 8^2 = 8*8 = 64
• 9^2 = 9*9 = 81

Since 75 is between 64 and 81, this means $\sqrt{75}$ is between 8 and 9

Put another way, we can say this:

$64 < 75 < 81\\\\\sqrt{64} < \sqrt{75} < \sqrt{81}\\\\\sqrt{8^2} < \sqrt{75} < \sqrt{9^2}\\\\8 < \sqrt{75} < 9$

Or we could use a calculator to find that:

• $\sqrt{75} \approx 8.66$
• $\sqrt{100} = 10$

Which is another way to see why $\sqrt{75}$ is between 8 and 9.