Rewrite the irrational square root 48−−√ as the product of an integer and another irrational square root.(1 point) Responses 43–√ 4 start root 3 end root 412−−√ 4 start root 12 end root 212−−√ 2 start root 12 end root 224−−√
√48 can be rewritten as √16 * √3, since 16 is a perfect square.
Therefore, the irrational square root of 48 can be expressed as 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.
Since 48 can be divided by 16 (which is a perfect square) without leaving a remainder, we can write it as:
√48 = √(16 * 3)
Taking the square root of 16 gives us 4:
√(16 * 3) = 4√3
Therefore, the irrational square root √48 can be rewritten as the product of an integer (4) and another irrational square root (√3):
√48 = 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 largest perfect square that divides evenly into 48. In this case, the largest perfect square is 16, which is equal to 4².
We can rewrite 48 as the product of 16 and 3: 48 = 16 * 3.
Now, let's rewrite the square root of 48 using this decomposition:
√48 = √(16 * 3)
Since the square root of 16 is 4, we can express it as:
√(16 * 3) = √16 * √3 = 4√3.
Therefore, the irrational square root √48 can be rewritten as the product 4√3, where 4 is an integer and √3 is another irrational square root.