Question

a square garden plot has an area of 24 ft2. a. find the length of each side in simplest radical form. b. calculate the length of each side to the nearest tenth of a foot.

Answer 1

The area of a square is equal to the side squared.

$s^{2} = A$

We can plug in 24 for A and then take the square root of each side to

find s.

$s^{2} = 24$

$s = \sqrt{24}$

We can simplify √24.

The prime factorization of 24 is 2 x 2 x 2 x 3.

Since we have 2 x 2 inside the radical we can simplify to have 2

outside the racial.

$\sqrt{24} = \sqrt{4*6} = 2 \sqrt{6}$

We can then use a calculator to find an approximate decimal value

2√6.

(You could technically calculate it by hend using the Babylonian

method, I don't think youre expectited to do that, though)

$2\sqrt{6} = 4.9 ft$