Rewrite the irrational square root √48 as the product of an integer and another irrational square root.(1 point)
√48 can be rewritten as √(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 can first simplify the square root of 48.
We can find the prime factorization of 48: 48 = 2 * 2 * 2 * 2 * 3.
Now, we can rewrite the square root of 48 as √(2 * 2 * 2 * 2 * 3).
Using the property of square roots (√(a * b) = √a * √b), we can split the square root as follows:
√(2 * 2 * 2 * 2 * 3) = √2 * √2 * √2 * √2 * √3
Simplifying, we have:
= 2 * 2 * √3
Therefore, the irrational square root √48 can be written as the product of an integer and another irrational square root as 4√3.
To rewrite the irrational square root √48 as the product of an integer and another irrational square root, we can start by finding the prime factorization of 48.
The prime factorization of 48 is:
48 = 2 * 2 * 2 * 2 * 3.
Now, let's simplify the square root of 48 using the prime factorization:
√48 = √(2 * 2 * 2 * 2 * 3)
We can pair up the prime factors into perfect squares:
√(2 * 2 * 2 * 2 * 3) = √(2 * 2 * 2 * 2) * √3
The square root of the perfect squares simplifies to an integer:
√(2 * 2 * 2 * 2) = 2 * 2 = 4
Putting it all together:
√48 = 4√3
So, the irrational square root √48 can be rewritten as the product of the integer 4 and the irrational square root √3.