​

Question

is not a whole number because there is no whole number that we can multiply by itself to find a product of 45. That means
45
​
is irrational, so we can only find an approximation of its value. To help us do that, we can start by finding the two perfect squares that 45 is between. Start by completing the table with the squares of 5, 6, 7, 8, and 9.
Squares
5
2
=
6
2
=
7
2
=
8
2
=
9
2
=

Answer 1

To find the perfect squares of the numbers 5 through 9, we can calculate each square as follows:

• \(5^2 = 25\)
• \(6^2 = 36\)
• \(7^2 = 49\)
• \(8^2 = 64\)
• \(9^2 = 81\)

Now we can fill in the table:

| Numbers | Squares | |---------|----------| | 5 | 25 | | 6 | 36 | | 7 | 49 | | 8 | 64 | | 9 | 81 |

Since \(45\) is between \(36\) (which is \(6^2\)) and \(49\) (which is \(7^2\)), we can conclude that:

\[ 6 < \sqrt{45} < 7 \]

To approximate \(\sqrt{45}\), we can use the fact that it is closer to \(6\) than to \(7\).