Question

The square root of a number is between 7 and 8. Which could be the number? *

Quadratics
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asked 2020-12-17
The square root of a number is between 7 and 8. Which could be the number? *

Answers (1)

2020-12-18

Let x be the number. If the square root of the number is between 7 and 8, then \(\displaystyle{7}{<}\sqrt{{{x}}}{<}{8}\).
Squaring all sides of the inequality gives \(\displaystyle{7}^{{{2}}}{<}\sqrt{{{x}}}^{{{2}}}{<}{8}^{{{2}}}\), which simplifies to \(\displaystyle{49}{<}{x}{<}{64}\)x can then be any number such that \(\displaystyle{49}{<}{x}{<}{64}\).

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