Question

(a) Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify $\sqrt{288}$to determine the length and the width of his garden. Round to the nearest tenth of a foot.

(b) Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify $\sqrt{288}-5$to determine the length and width of the new garden. Round to the nearest tenth of a foot.

Short answer

Part (a)$\approx 17\mathrm{ft}$

Part (b)$\approx 12\mathrm{ft}$

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Elliott decides to construct a square garden that will take up 288 square feet of his yard.

We have to simplify $\sqrt{288}$to determine the length and the width of his garden.

Part (a) Step 2. Simplify the given expression 288.

$\sqrt{288}$

Rewrite the radical as a product using the largest perfect square factor,

$\sqrt{144·2}$

Rewrite the radical as a product of two radicals,

$\sqrt{144}·\sqrt{2}$

Simplify,

localid="1648303737526" $12\sqrt{2}\approx 16.97$

The length and the width of the garden are around 17 ft.

Part (b) Step 1. Given information.

Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden.

We have to simplify $\sqrt{288}-5$ to determine the length and the width of the new garden.

Part (b) Step 2. Simplify the given expression 288-5.

$\sqrt{288}-5$

Rewrite the radical as a product using the largest perfect square factor,

$\sqrt{144·2}-5$

Rewrite the radical as a product of two radicals,

$\sqrt{144}·\sqrt{2}-5$

Simplify,

role="math" localid="1648304235610" $12\sqrt{2}-5\approx 12\mathrm{ft}$

The length and width of the new garden are around 12 ft.