Question

A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?

Answer 1

The length of the side of the square is approximately
`17.32` feet, which lies between the whole numbers
`17` and
`18`.

Explanation:

Step 1: Assume your variable

Since all the sides of a square are the same, let's consider the side to be the variable:
`x`.

Step 2: Create an equation

The formula for the area of a square is:

`\text{Area}=\text{Side}^(2)`

We have assumed the side to be
`x`, and the area is said to be
`300`, so substitute these values into the formula:

`\text{Area}=\text{Side}^(2)\\300=x^(2)`

Step 3: Solve the equation

Using the formula for the area of a square, we came to find an equation:

`x^(2)=300`

Now, let's find the value of
`x`:

`x^(2)=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^(2)}=√(300)\\\\\text{Simplify:}\\x=√(300)\\\\\text{Calculate:}\\x\approx 17.32`

The length of the side of the square is approximately
`17.32` feet.

As we know, this number lies between
`17` and
`18`.

Answer 2

Area = 300 ft^2

Formula

Area = length of a side x length of a side

Substitution

300 = length of a side ^2

`√(300)`
`√(300)\text{ = 17.32}`

The length of a side is between 17 and 18