Find the cube root of —125³√—125
The cube root of -125 is -5.
To find the cube root of -125, we need to consider the properties of cube roots.
The cube root is a value that, when multiplied by itself three times, equals the original number. In this case, we need to find a number whose cube is equal to -125.
Since -125 is a negative number, we know that its cube root will also be negative.
To find the cube root of -125, we can write it as (-125)^(1/3).
Using the exponent property, we can rewrite it as (-125)^(1/3) = (-1)^3 * (125)^(1/3).
Now we can evaluate the cube root of 125. The cube root of 125 is 5 because 5 * 5 * 5 = 125.
Substituting this value back into our equation, we have (-1)^3 * 5.
Evaluating (-1)^3, we get -1.
Therefore, the cube root of -125 is -5.
To find the cube root of -125 (denoted as ∛-125), we can follow these steps:
Step 1: Determine the sign of the answer
In this case, the given number is -125, which means it is negative. Since any number raised to an odd power maintains its sign, the cube root of -125 will also be negative.
Step 2: Calculate the magnitude of the cube root
To calculate the magnitude of the cube root of 125 (∛125), we need to identify the largest perfect cube that is less than or equal to 125. In this case, the largest perfect cube is 125 itself, as 5³ = 125.
Step 3: Apply the sign obtained in Step 1
Since the given number is negative, the cube root will be negative. Thus, the cube root of -125 is -∛125.
Hence, the cube root of -125 is -∛125.