Find the cube root of -125: ^3√-125
The cube root of -125 is -5.
To find the cube root of -125 (written as ^3√-125), follow these steps:
Step 1: Determine the sign
Since -125 is a negative number, the cube root will also be negative.
Step 2: Find the absolute value
The absolute value of -125 is 125.
Step 3: Find the cube root of the absolute value
The cube root of 125 is 5, because 5 * 5 * 5 equals 125.
Step 4: Add the negative sign
Since we determined the cube root of -125 to be negative in step 1, the final answer is -5.
Therefore, the cube root of -125 (^3√-125) is -5.
To find the cube root of -125, we can follow these steps:
Step 1: Write the given number as a negative number raised to a power.
-125 = -1 * 125
Step 2: Express the number inside the cube root in terms of its prime factorization.
125 = 5 * 5 * 5
Step 3: Rewrite the number using the prime factorization from Step 2.
-125 = -1 * (5 * 5 * 5)
Step 4: Take the cube root of each factor individually using the property of exponents.
^3√(-125) = -1 * ^3√(5 * 5 * 5)
Step 5: Simplify the expression within the cube root.
^3√(5 * 5 * 5) = ^3√(5^3) = 5
Step 6: Put the negative sign back to the result obtained in Step 5.
^3√(-125) = -5
So, the cube root of -125 is -5.