Rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root.(1 point)
^3√48 can be written as 2 * ^3√(4 * 12) or 2 * ^3√(4 * 3^2).
To rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root, we can start by finding the greatest perfect cube that divides 48. The largest perfect cube that divides 48 is 8, which is equal to 2^3.
Therefore, we can rewrite ^3√48 as ^3√(2^3 * 6).
This can be further simplified as ^3√(2^3) * ^3√6, which equals 2 * ^3√6.
Therefore, ^3√48 can be rewritten as a product of an integer (2) and another irrational cube root (^3√6).
To rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root, we need to factor the number 48 and look for any perfect cube factors.
To start, we can recognize that 48 can be expressed as the product of 2 and 24:
48 = 2 × 24
Now, let's continue factoring 24. We see that 24 can be expressed as the product of 2 and 12:
24 = 2 × 12
Next, let's continue factoring 12. We can again express it as the product of 2 and 6:
12 = 2 × 6
Now, we can see that 6 itself is a perfect cube since 6 = 2 × 3.
Therefore, we can rewrite the original irrational cube root as:
^3√48 = ^3√(2 × 2 × 2 × 3)
Now, we can rewrite this as a product of an integer and another irrational cube root:
^3√48 = 2 × ^3√(2 × 3)
So, ^3√48 can be rewritten as 2 times the irrational cube root of 6.