Question

Approximate the irrational number √5 to two decimal places. It is approximately what?

a) 2.23
b) 2.24
c) 2.25
d) 2.26

Answer 1

The square root of 5, an irrational number, is approximately 2.236. When rounded to two decimal places, considering that the third decimal place is a 6, it rounds up to 2.24.

Step-by-step explanation:

To approximate the irrational number √5 to two decimal places, we first need to understand what √5 means. The square root of 5 is the number, which when multiplied by itself, gives the product 5. This number is not a perfect square, thus its square root is an irrational number, which means it cannot be exactly expressed as a fraction and its decimal representation is non-terminating and non-repeating.

Using a calculator, when we compute √5, we get a decimal that goes on indefinitely. For the purpose of approximation to two decimal places, however, we would round based on the third decimal place. In this case, √5 is approximately 2.236. To round to two decimal places, we look at the third decimal place, which is a 6, meaning we round up. Thus, √5 rounded to two decimal places is approximately 2.24, which corresponds to the option (b).