Rewrite the irrational square root √48 as the product of an integer and another irrational square root.
1. 4√12
2. 2√12
3. 2√24
4. 4√3
3. 2√24
To rewrite √48 as the product of an integer and another irrational square root, we need to find the largest perfect square that divides evenly into 48.
Since 16 is the largest perfect square that divides evenly into 48, we can rewrite √48 as √16 * √3.
The square root of 16 is 4, which is an integer, and the square root of 3 is an irrational number.
Therefore, the correct answer is option 4: 4√3.
To rewrite the irrational square root √48 as the product of an integer and another irrational square root, we need to find a perfect square that divides 48.
Breaking down 48 into its prime factors, we have: 48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3.
Since there are four 2's, we can take two of them and write them as a perfect square: 2^2 = 4.
Now, we can rewrite √48 as: √(2^4 * 3) = √(2^2 * 2^2 * 3) = (2 * 2)√3 = 4√3.
Therefore, the answer is 4√3, option 4.