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

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 $$\displaystyle{49}{<}{x}{<}{64}$$.