Question
convert 3.6342 into a square root number
Answers
Answer
rewrite the irrational cube root 48 as a product of an integer and another irrational cube root
Answer
the options are
2^3√6
-2^3√6
4^3√12
4^3√3
2^3√6
-2^3√6
4^3√12
4^3√3
Answer
what is the irrational cube root of ^3√-24 rewritten as a product of an integer and another irrational cube root
Answer
the options are
2^3√6
-2^3√4
2^3√3
-2^3√3
2^3√6
-2^3√4
2^3√3
-2^3√3
Answered by
GPT 3.5
To convert 3.6342 into a square root number, we need to find a perfect square that is closest to this decimal number.
The nearest perfect square is 4 (2^2 = 4), which has a square root of 2.
So, 3.6342 is approximately equal to √4 = 2.
The nearest perfect square is 4 (2^2 = 4), which has a square root of 2.
So, 3.6342 is approximately equal to √4 = 2.
Answered by
GPT 3.5
To rewrite the irrational cube root of 48 as a product of an integer and another irrational cube root, we can factorize 48 to simplify the expression.
First, let's find the prime factors of 48:
48 = 2 * 2 * 2 * 2 * 3
Now, we can rewrite the cube root of 48 as:
∛48 = ∛(2 * 2 * 2 * 2 * 3)
Since there are three 2's, we can take one of them out as a factor. This leaves us with:
∛48 = 2 * ∛(2 * 2 * 3)
Simplifying further, we have:
∛48 = 2∛(12)
So, the irrational cube root of 48 can be written as the product of 2 and the cube root of 12.
First, let's find the prime factors of 48:
48 = 2 * 2 * 2 * 2 * 3
Now, we can rewrite the cube root of 48 as:
∛48 = ∛(2 * 2 * 2 * 2 * 3)
Since there are three 2's, we can take one of them out as a factor. This leaves us with:
∛48 = 2 * ∛(2 * 2 * 3)
Simplifying further, we have:
∛48 = 2∛(12)
So, the irrational cube root of 48 can be written as the product of 2 and the cube root of 12.
Answered by
GPT 3.5
To rewrite the irrational cube root of 48 as a product of an integer and another irrational cube root, we need to find a perfect cube that is a factor of 48.
Let's examine the options given:
1) 2^3√6: This expression does not involve 48, so it is not a valid option.
2) -2^3√6: This expression also does not involve 48, so it is not a valid option.
3) 4^3√12: Let's evaluate this option.
4^3√12 = 64√12
However, 64 is not a factor of 48, so this is not the correct option.
4) 4^3√3: Let's evaluate this option.
4^3√3 = 64√3
Similarly, 64 is not a factor of 48, so this is not the correct option.
Since none of the given options work, we can conclude that the irrational cube root of 48 cannot be expressed as a product of an integer and another irrational cube root using the options provided.
Let's examine the options given:
1) 2^3√6: This expression does not involve 48, so it is not a valid option.
2) -2^3√6: This expression also does not involve 48, so it is not a valid option.
3) 4^3√12: Let's evaluate this option.
4^3√12 = 64√12
However, 64 is not a factor of 48, so this is not the correct option.
4) 4^3√3: Let's evaluate this option.
4^3√3 = 64√3
Similarly, 64 is not a factor of 48, so this is not the correct option.
Since none of the given options work, we can conclude that the irrational cube root of 48 cannot be expressed as a product of an integer and another irrational cube root using the options provided.
Answered by
GPT 3.5
To rewrite the irrational cube root of ^3√-24 as a product of an integer and another irrational cube root, we need to factorize -24.
First, let's find the prime factors of 24:
24 = 2 * 2 * 2 * 3
Now, we can rewrite the cube root of -24 as:
^3√-24 = ^3√(2 * 2 * 2 * 3)
Since there are three 2's, we can take one of them out as a factor. This leaves us with:
^3√-24 = -2 * ^3√(2 * 2 * 3)
Simplifying further, we have:
^3√-24 = -2 * ^3√(12)
So, the irrational cube root of -24 can be written as the product of -2 and the cube root of 12.
First, let's find the prime factors of 24:
24 = 2 * 2 * 2 * 3
Now, we can rewrite the cube root of -24 as:
^3√-24 = ^3√(2 * 2 * 2 * 3)
Since there are three 2's, we can take one of them out as a factor. This leaves us with:
^3√-24 = -2 * ^3√(2 * 2 * 3)
Simplifying further, we have:
^3√-24 = -2 * ^3√(12)
So, the irrational cube root of -24 can be written as the product of -2 and the cube root of 12.
Answered by
GPT 3.5
To rewrite the irrational cube root of ^3√-24 as a product of an integer and another irrational cube root, let's examine the given options:
1) 2^3√6: This expression does not involve -24, so it is not a valid option.
2) -2^3√4: This expression involves -24, but it has 4 inside the cube root instead of 24. Hence, it is not the correct option.
3) 2^3√3: This expression also contains 3 inside the cube root, but it does not have the negative sign. It is not the correct option.
4) -2^3√3: This option involves -24 and has 3 inside the cube root. So, let's evaluate it:
-2^3√3 = -2 * ^3√3
Therefore, the irrational cube root of -24 can be rewritten as the product of -2 and ^3√3. Thus, the correct option is -2^3√3.
1) 2^3√6: This expression does not involve -24, so it is not a valid option.
2) -2^3√4: This expression involves -24, but it has 4 inside the cube root instead of 24. Hence, it is not the correct option.
3) 2^3√3: This expression also contains 3 inside the cube root, but it does not have the negative sign. It is not the correct option.
4) -2^3√3: This option involves -24 and has 3 inside the cube root. So, let's evaluate it:
-2^3√3 = -2 * ^3√3
Therefore, the irrational cube root of -24 can be rewritten as the product of -2 and ^3√3. Thus, the correct option is -2^3√3.
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