Rewrite the irrational square root √48 as the product of an integer and another irrational square root.(1 point)
Responses
412−−√
4 start root 12 end root
43–√
4 start root 3 end root
212−−√
2 start root 12 end root
224−−√
4√3
What is the irrational square root √28 simplified?(1 point)
Responses
47–√
4 start root 7 end root
214−−√
2 start root 14 end root
27–√
2 start root 7 end root
4–√ ⋅ 7–√
2√7
Question
Rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root.(1 point)
Responses
43–√3
4 root index 3 start root 3 end root
−26–√3
negative 2 root index 3 start root 6 end root
412−−√3
4 root index 3 start root 12 end root
26–√3
2√3
What is the irrational cube root ^3√-24 rewritten as a product of an integer and another irrational cube root?(1 point)
Responses
−24–√3
negative 2 root index 3 start root 4 end root
26–√3
2 root index 3 start root 6 end root
23–√3
2 root index 3 start root 3 end root
−23–√3
negative 2 root index 3 start root 3 end root
-2√3
What is the irrational cube root ^3/40 rewritten as a product of an integer and another irrational cube root?(1 point)
210−−√3
2 root index 3 start root 10 end root
25–√3
2 root index 3 start root 5 end root
85–√3
8 root index 3 start root 5 end root
−25–√3
2√3/5
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 prime factorization of 48 is 2^4 * 3. We can see that 16 (which is 2^4) is a perfect square factor of 48.
Now, we can rewrite √48 as √(16 * 3). Using the property √(xy) = √x * √y, we can split the square root:
√48 = √(16) * √(3)
Simplifying the square root of 16, we know that √16 = 4. So, we have:
√48 = 4 * √(3)
Therefore, the irrational square root √48 can be rewritten as the product of an integer (4) and another irrational square root (√3).