Question

Johnny wants to estimate the √{27} without a calculator. He estimates that it is around 5.6. Explain what is wrong with Johnny's estimation.

a) Johnny's estimation is accurate.

b) Johnny's estimation is too high.

c) Johnny's estimation is too low.

d) Johnny's estimation is correct.

Answer 1

Johnny's estimation of the square root of 27 as 5.6 is too high. The correct estimation should be slightly more than 5, as 27 is closer to the perfect square of 25.

Step-by-step explanation:

Johnny wants to estimate the square root of 27 without a calculator and believes it is around 5.6. This estimation is incorrect. To understand why, we should consider the perfect squares closest to 27, which are 25 (5 squared) and 36 (6 squared). Since 27 is closer to 25, the accurate estimation of the square root of 27 would be slightly more than 5. Therefore, Johnny's estimation is too high, as the true value is between 5 and 6 but closer to 5.