Question

Use the "squeeze" strategy to approximate the following:
`\sqrt[3]{107}`(round to the nearest integer as needed)

Answer 1

∛(107) ≅ 5

Step-by-step explanation

The squeeze approach uses approximations of perfect cubes around the number to approximate its cube roots.

Let the cube root of 107 be x

∛(107) = x

x³ = 107

We can then write the perfect cubes around this number

2³ = 8

3³ = 27

4³ = 64

5³ = 125

We can easily see that 107 is between the two perfect cube numbers 64 and 125.

Since 107 is far closer to 125 than 64, the closest approximation for ∛(107) will be x = 5

∛(107) ≅ 5

5³ ≅ 107

Hope this Helps!!!