Question

Which of these numbers is greater than 6 but less than 7 ? A. 6.5\sqrt{6.5} B. 67\sqrt{67} C. 45\sqrt{45} D. 76\sqrt{76}

Solution

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Since 62=366^2=36 and 72=497^2=49, then 6=366=\sqrt{36} and 7=497=\sqrt{49}. You therefore need to find what number is between 36\sqrt{36} and 49\sqrt{49}. From the answer choices, only 45\sqrt{45} lies between 36\sqrt{36} and 49\sqrt{49} so the correct answer is C. 45\sqrt{45}.

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