what is ^3√-72 simplified
The cube root of -72 simplified is -4.
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To simplify the cube root of -72, we can break it down as follows:
^3√(-72) = ^3√(-1 * 36 * 2)
Now, we know that the cube root of -1 is -1, and the cube root of 36 is 3. Therefore:
^3√(-72) = -1 * 3 * ^3√2 = -3√2.
So, the simplified form of ^3√-72 is -3√2.
To simplify the expression ^3√-72, follow these steps:
Step 1: Determine if the number inside the radical (^3√-72) is a perfect cube.
In this case, -72 is not a perfect cube since there is no whole number that can be multiplied by itself three times to equal -72.
Step 2: Rewrite the expression using a factor of -72.
Since -72 is divisible by -8, you can rewrite the expression as ^3√(-8 × 9).
Step 3: Simplify the cube root of -8.
Since -8 is a perfect cube (-2 × -2 × -2 = -8), you can simplify ^3√(-8) as -2.
Step 4: Simplify the remaining factor of 9.
The cube root of 9 is not a perfect cube, so it cannot be simplified any further.
Step 5: Combine the simplified factors.
You combine the simplified factors -2 and 9 to get the final result.
Therefore, ^3√-72 is simplified as -2 * ^3√9 (or -2√9).
To simplify the expression ^3√-72, we need to evaluate the cube root of -72.
Step 1: Find the prime factorization of 72.
The prime factorization of 72 is 2^3 * 3^2.
Step 2: Determine the sign of the result.
Since we are dealing with the cube root of -72, the result will be negative.
Step 3: Simplify the cube root.
We can rewrite ^3√-72 as ^3√(-1 * 2^3 * 3^2).
Now, we can simplify the cube root by breaking down the expression into smaller cube roots of each factor:
^3√(-1) * ^3√(2^3) * ^3√(3^2).
Step 4: Evaluate each of the cube roots.
^3√(-1) = -1 (since the cube root of -1 is -1).
Next, ^3√(2^3) = ^3√8 = 2 (since 2^3 equals 8).
Lastly, ^3√(3^2) = ^3√9 = 3 (since 3^2 equals 9).
Step 5: Combine the results.
We multiply the individual cube roots together:
-1 * 2 * 3 = -6.
Therefore, ^3√-72 simplifies to -6.