Question

Arrange the following numbers in ascending order:

a) √75
b) √45
c) 7.12 (repeating)
d) 89

Answer 1

To arrange the numbers √75, √45, 7.12 (repeating), and 89 in ascending order, we first approximate the square roots and then compare them. In ascending order, the numbers are √45, 7.12 (repeating), √75, and finally 89.

Step-by-step explanation:

The question asks us to arrange the following numbers in ascending order: √75, √45, 7.12 (repeating), and 89. To solve this, we need to first evaluate or estimate the square roots and compare them to the given number which has a repeating decimal.

• Firstly, √75 is approximately 8.66, since 8.66² = 75.
• Secondly, √45 is approximately 6.71, because 6.71² = 44.99, which is close to 45.
• The number 7.12 (repeating) is just 7.12 since the decimal repeats the digit 2 indefinitely.

Next, we compare these numbers with 89:

1. √45 (approximately 6.71)
2. 7.12 (repeating)
3. √75 (approximately 8.66)
4. 89

Therefore, the numbers in ascending order are: √45, 7.12 (repeating), √75, and then 89.