Simplify ³√40
The cube root of 40 simplifies to 40^(1/3).
To simplify the cube root of 40, we need to find the highest perfect cube that divides evenly into 40.
The prime factorization of 40 is: 2 × 2 × 2 × 5.
We can group the factors of 40 into sets of three: (2 × 2 × 2) and 5.
Simplifying the cube root of 40, we have:
³√40 = ³√(2 × 2 × 2 × 5) = 2 × ∛5 = 2∛5
Therefore, the simplified form of the cube root of 40 is 2∛5.
To simplify the cube root of 40, you need to find the prime factorization of 40.
Start by dividing 40 by the smallest prime number, which is 2. You get:
40 ÷ 2 = 20
Now, divide 20 by 2 again:
20 ÷ 2 = 10
Notice that both 2 and 2 divide evenly into 40, so you write them down as factors:
40 = 2 × 2 × 10
Next, divide 10 by the next prime number, which is 5:
10 ÷ 5 = 2
Now, write down 5 as a factor because it divides evenly into 10:
40 = 2 × 2 × 5 × 2
To simplify the cube root, look for groups of three identical factors. In this case, there are three factors of 2:
(2 × 2 × 2) × 5
This can be written as:
2³ × 5
So, the simplified cube root of 40 is:
³√40 = 2√5