Question

Write the exact value of the side length of each square. If the value is not a whole number, estimate the length.
area exact side length estimite side length
100 square units ------ units
95 square units bettween ----- and -----
36 square units -------units
30 square units bettween ----- and -----

Answer 1

Given:

The area of the squares are given.

To find:

The exact side length or estimate side length of the square.

Solution:

We know that, the area of a square is

$A=a^2$

Where, a is the side length of the square.

$a=\sqrt{A}$

Area of the square is 100 square units. So, the side length is:

$a=\sqrt{100}$

$a=10$

Therefore, the side length is 10 units.

Area of the square is 95 square units. So, the side length is:

$a=\sqrt{95}$

It is not exact. We know that $\sqrt{81}<\sqrt{95}<\sqrt{100}$.

Therefore, the side length is between 9 and 10.

Area of the square is 36 square units. So, the side length is:

$a=\sqrt{36}$

$a=6$

Therefore, the side length is 6 units.

Area of the square is 30 square units. So, the side length is:

$a=\sqrt{30}$

It is not exact. We know that $\sqrt{25}<\sqrt{30}<\sqrt{36}$.

Therefore, the side length is between 5 and 6.