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Algebra Difficulty 1.6 Junior Find the answer

Which of the following is closest in value to 7?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

We note that 7=497=\sqrt{49} and that 40<49<50<60<70<80\sqrt{40}<\sqrt{49}<\sqrt{50}<\sqrt{60}<\sqrt{70}<\sqrt{80}.
This means that 40\sqrt{40} or 50\sqrt{50} is the closest to 7 of the given choices.
Since 406.32\sqrt{40} \approx 6.32 and 507.07\sqrt{50} \approx 7.07, then 50\sqrt{50} is closest to 7.

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