Rewrite the irrational square root sqrt(48) as the product of an integer and another irrational square root
(1 point)
© 2sqrt(24)
4sqrt(3)
2sqrt(12)
O 4sqrt(12)
4√(3)
To rewrite the irrational square root sqrt(48) as the product of an integer and another irrational square root, we can simplify the square root of 48 by factoring out perfect squares from the number.
Let's start by finding the perfect squares that divide 48:
- 4 is a perfect square that divides 48.
- 12 is also a perfect square that divides 48.
So, we can rewrite sqrt(48) as the product of sqrt(4) and sqrt(12):
sqrt(48) = sqrt(4 * 12)
Simplifying further, we have:
sqrt(48) = sqrt(4) * sqrt(12)
sqrt(48) = 2 * sqrt(12)
Therefore, the irrational square root sqrt(48) can be rewritten as the product of an integer and another irrational square root, which is 2sqrt(12).
To rewrite the irrational square root √48 as the product of an integer and another irrational square root, we need to simplify the square root as much as possible.
First, let's find the prime factors of 48.
48 can be expressed as:
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Now, let's rewrite √48 using these prime factors:
√48 = √(2^4 * 3)
Since the square root of a product is equal to the product of the square roots of each factor, we can split the square root of 48:
√48 = √(2^4 * 3) = √(2^4) * √3
Simplifying each square root:
√(2^4) = 2^2 = 4
√3 remains as √3
Therefore, the square root √48 can be rewritten as the product of an integer and another irrational square root:
√48 = 4√3
So, the correct answer is 4√3.