Question

Arrange √75 , √45 , and 7.12 in order.

a) √45 < √75 < 7.12
b) √45 < 7.12 < √75
c) 7.12 < √45 < √75
d) 7.12 < √75 < √45

Answer 1

The square root values and the decimal number are compared by simplifying the square roots and estimating their values. The correct order is √45 < 7.12 < √75.

Step-by-step explanation:

To compare the square roots and the decimal number, we need to simplify the square roots or estimate their decimal values and then compare them with the given decimal number 7.12.

• √75 can be simplified to √(25 × 3) which equals 5√3. The approximate value of √3 is 1.73, so 5√3 is approximately 5 × 1.73 = 8.65.
• √45 can be simplified to √(9 × 5) which equals 3√5. The approximate value of √5 is 2.24, so 3√5 is approximately 3 × 2.24 = 6.72.

Comparing these values, we find that 6.72 (√45) < 7.12 < 8.65 (√75). Therefore, the correct answer is b) √45 < 7.12 < √75.