What is the irrational square root √28 simplified?
A. 2√14
B. 4√7
C. 2√7
D. √4 * √7
1. 4√3
2. 2√7
3. 2³√6
4. -2³√3
5. 2³√5
are the correct answers
To simplify √28, we look for the perfect squares that can be factored out from under the square root sign. The largest perfect square that can be factored out from 28 is 4, which is the square of 2. Thus, √28 can be simplified as √4 * √7. Simplifying the square root of 4 gives us 2, so the simplified form is 2√7. Therefore, the answer is C.
Rewrite the irrational cube root ³√48 as a product of an integer and another irrational cube root.
A. 4³√12
B. 2³√6
C. -2³√6
D. 4³√3
To rewrite ³√48 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that can be factored out from under the cube root sign. The largest perfect cube that can be factored out from 48 is 8, which is the cube of 2. Thus, ³√48 can be rewritten as ³√8 * ³√6. Simplifying the cube root of 8 gives us 2, so the rewritten form is 2 * ³√6.
Therefore, the answer is B.
What is the irrational cube root ³√-24 rewritten as a product of an integer and another irrational cube root?
A. -2³√4
B. -2³√3
C. 2³√6
D. 2³√3
To rewrite ³√-24 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that can be factored out from under the cube root sign. In this case, we know that (-2)³ = -8, so we can factor (-8) out from under the cube root sign. Therefore, ³√-24 can be rewritten as (-2) * ³√3.
The answer is B.
What is the irrational cube root ³√40 rewritten as a product of an integer and another irrational cube root?
A. 8³√5
B. 2³√10
C. -2³√5
D. 2³√5
To rewrite ³√40 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that can be factored out from under the cube root sign. In this case, we know that 2³ = 8, so we can factor 8 out from under the cube root sign. Therefore, ³√40 can be rewritten as 2 * ³√5.
The answer is D.
Apologies for the previous incorrect response.
Here are the correct answers:
1. √28 simplified is 2√7.
2. The irrational cube root ³√48 rewritten as a product of an integer and another irrational cube root is 2³√6.
3. The irrational cube root ³√-24 rewritten as a product of an integer and another irrational cube root is -2³√3.
4. The irrational cube root ³√40 rewritten as a product of an integer and another irrational cube root is 2³√5.