Question

Which of the following is a true statement?

A) <√65<8
B) 2 <√ 7<3
C) 10<√95<11

Answer 1

The true statement among the options given is B) 2 <√7<3. We can determine this by squaring the whole numbers to compare them with the numbers under the square root.

Step-by-step explanation:

To determine the true statement, we can approximate the square roots or square the given numbers to see if the inequalities hold. Statement A is false since √65 is greater than 8 because 8 squared is 64, and 65 is greater than 64. Statement B is true because 2 squared is 4 3 squared is 9, and 7 falls between these two squares, making 2<√7<3 true. Statement C is false because 10 squared is 100 and 11 squared is 121, and since 95 falls between 100 and 121, √95 should fall between 10 and 11, but the inequality is reversed; it should be 10<√95<11. Therefore, the correct answer is: B) 2 <√7<3.