rewrite the irrational square root of 48 as the product of an integer and another irrational square root
Let's rewrite the irrational square root of 48 as the product of an integer and another irrational square root.
First, let's find the largest perfect square that divides evenly into 48. The largest perfect square that divides evenly into 48 is 16 (4 * 4 = 16), leaving us with a remaining factor of 3.
Now, we can rewrite the square root of 48 as follows:
√48 = √(16 * 3)
We can split the square root of 16 from the remaining factor of 3:
√(16 * 3) = √16 * √3
Simplifying the square root of 16 gives us:
√16 = 4
Thus, we can rewrite the irrational square root of 48 as the product of an integer and another irrational square root:
√48 = 4√3
What is the irrational square root 28−−√ simplified?
To simplify the irrational square root of 28 (√28), we need to find the largest perfect square that divides evenly into 28. The largest perfect square that divides into 28 is 4 (2 * 2 = 4).
Now, we can rewrite √28 as follows:
√28 = √(4 * 7)
Separating the square root of 4 and the remaining factor of 7, we have:
√(4 * 7) = √4 * √7
Simplifying the square root of 4 gives us:
√4 = 2
Therefore, the simplified form of the irrational square root of 28 (√28) is:
√28 = 2√7
Rewrite the irrational cube root 48−−√3 as a product of an integer and another irrational cube root.
To rewrite the irrational cube root of 48 (∛48) as a product of an integer and another irrational cube root, we need to find the largest perfect cube that divides evenly into 48. The largest perfect cube that divides into 48 is 8 (2^3 = 8).
Now, let's rewrite ∛48 as follows:
∛48 = ∛(8 * 6)
Splitting the cube root of 8 from the remaining factor of 6, we have:
∛(8 * 6) = ∛8 * ∛6
Simplifying the cube root of 8 gives us:
∛8 = 2
Therefore, we can rewrite the irrational cube root of 48 (∛48) as the product of an integer and another irrational cube root:
∛48 = 2∛6
What is the irrational cube root −24−−−−√3 rewritten as a product of an integer and another irrational cube root?
To rewrite the irrational cube root of -24 (∛-24) as a product of an integer and another irrational cube root, we need to find the largest perfect cube that divides evenly into -24. The largest perfect cube that divides into -24 is -8 (-2^3 = -8).
Now, let's rewrite ∛-24 as follows:
∛-24 = -∛(8 * 3)
Splitting the cube root of 8 from the remaining factor of 3, we have:
-∛(8 * 3) = -∛8 * ∛3
Simplifying the cube root of 8 gives us:
-∛8 = -2
Therefore, we can rewrite the irrational cube root of -24 (∛-24) as the product of an integer and another irrational cube root:
∛-24 = -2∛3