Question

The edge length of a cube-shaped box is 2√5 inches long. Estimate the length of the edge to the nearest tenth of an inch. Then explain why you can only estimate this length, not find its exact value.

Answer 1

a) 4.5 inches

b) 2√5 is irrational

Explanation:

It was given that the edge length of a cube-shaped box is 2√5 inches long.

To estimate the length of the edge to the nearest tenth of an inch, we change √5 to decimals to obtain:

`2 √(5) \approx2(2.26067977.....)`

`2 √(5) \approx4.47213955.....`

`2 √(5) \approx4.5`

When we round to the nearest tenth, we obtain 4.5

We cannot find its exact value because √5 is an irrational number.

The product of a rational and an irrational number is irrational.