Question

Find the approximate side length of a square game board with an area of 105 in2.

Answer 1

Rounded to the nearest inch: 10

Rounded to the nearest tenth: 10.2

Rounded to the nearest hundredth: 10.25

Explanation:

To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!

`A=s^2`

We are given the area, so plugging that into our equation looks like this:

`105=s^2`

To eliminate the exponent, take the square root of both sides of the equation!

`√(105)=s`

From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.

The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.

105 is closer to 100 than to 121, so √105 is closer to √100.

√100 is equal to 10, so the √105 is approximately 10 inches!

Using a calculator to check:

`√(105)=10.247` inches