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:
`√(75)`

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Step-by-step 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
`√(75)` is between 8 and 9

Put another way, we can say this:

`64 < 75 < 81\\\\√(64) < √(75) < √(81)\\\\√(8^2) < √(75) < √(9^2)\\\\8 < √(75) < 9\\\\`

Or we could use a calculator to find that:

• 
  `√(75) \approx 8.66`
• 
  `√(100) = 10`

Which is another way to see why
`√(75)` is between 8 and 9.