Simplify:
5(cube root of 16) + 2(cube root of 54)
5 times the cube root of 16 plus 2 times the cube root of 54.
I do not know how to type in the radical signs. Sorry.
5∛16 + 2∛54
Try to find perfect cubes under the ∛
5∛(8*2) + 2∛(27*2)
5(∛8∛2) + 2(∛27∛2)
5(2∛2) + 2(3∛2)
10∛2 + 6∛2
16∛2
Need answer
To simplify the expression 5∛16 + 2∛54, we can start by finding the prime factorization of the numbers inside the cube roots:
1. Prime factorization of 16:
16 = 2 × 2 × 2 × 2 = 2^4
2. Prime factorization of 54:
54 = 2 × 3 × 3 × 3 = 2 × 3^3
Now, we can simplify the expression:
5∛16 + 2∛54
= 5∛(2^4) + 2∛(2 × 3^3)
= 5 × 2∛2 + 2 × 3∛3^2
= 10∛2 + 2 × 3 × 3∛3
= 10∛2 + 6∛3
So, the simplified form of the expression 5∛16 + 2∛54 is 10∛2 + 6∛3.
No problem! I can help you simplify the expression without the radical signs. Let's work step by step.
First, we'll simplify the cube roots individually. The cube root of 16 can be expressed as 16^(1/3), and the cube root of 54 can be expressed as 54^(1/3).
To simplify 16^(1/3), we need to find the cube root of 16. The cube root of 16 is 2 since 2 x 2 x 2 = 16. So, 16^(1/3) = 2.
To simplify 54^(1/3), we need to find the cube root of 54. It is not a perfect cube, so we can leave it as it is.
Now, let's substitute these simplified cube roots back into the expression:
5 * (cube root of 16) + 2 * (cube root of 54) becomes:
5 * 2 + 2 * (54^(1/3))
Next, we can simplify the product of 5 and 2, which is 10:
10 + 2 * (54^(1/3))
Lastly, we cannot simplify the cube root of 54 any further, so we leave it as it is. The final simplified expression is:
10 + 2 * (cube root of 54)