To approximate the square root of 56, we need to find the perfect squares that are closest to 56.
First, we note that 49 is a perfect square (since [tex]\( \sqrt{49} = 7 \)[/tex]) and it is the largest perfect square that is less than 56.
Next, we look for the nearest perfect square that is greater than 56. The perfect square closest to 56 on the higher side is 64 (since [tex]\( \sqrt{64} = 8 \)[/tex]).
Therefore, the inequality we are looking for is:
[tex]\[
\sqrt{49}<\sqrt{56}<\sqrt{64}
\][/tex]
Hence, the appropriate perfect squares to fill in the blanks are 49 and 64.
