Rewrite the irrational square root √48 as the product of an integer and another irrational square root.(1 point)
√48 = √(16 * 3) = √16 * √3 = 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 factor of 48.
The largest perfect square that divides 48 is 16 (4^2), so we can rewrite √48 as:
√48 = √(16 * 3)
We can separate the square root into two factors:
√(16 * 3) = √16 * √3
Simplifying further:
√16 * √3 = 4 * √3
Therefore, √48 can be rewritten as the product 4√3.
To rewrite the irrational square root √48 as the product of an integer and another irrational square root, we need to find the largest perfect square that is a factor of 48.
Start by breaking down 48 into its prime factors:
48 = 2 × 2 × 2 × 2 × 3
From these factors, we can form the square root of the largest perfect square that divides evenly into 48. In this case, the largest perfect square is 16 (4 × 4).
√48 = √(16 × 3)
Now, we can simplify further by factoring out the perfect square and writing the square root as the product of two square roots:
√48 = √16 × √3
Since √16 = 4, our final answer is:
√48 = 4√3