Find the cube root of −343 : −343−−−−√3
The cube root of −343 is -7.
To find the cube root of -343, we can follow these steps:
Step 1: Recognize that -343 can be written as (-7)^3.
Step 2: Take the cube root of (-7)^3.
Step 3: The cube root of a number is the value that, when multiplied by itself three times, gives the original number. So, the cube root of -343 is -7.
Therefore, the cube root of -343 is -7.
To find the cube root of -343, we can use the formula:
Cube root of a number = (number)^(1/3)
Applying this formula to -343, we get:
Cube root of -343 = (-343)^(1/3)
Now let's simplify this expression. We know that -343 can be written as (-7)^3. Therefore, we can rewrite the expression as:
Cube root of -343 = ((-7)^3)^(1/3)
Using the property of exponents (a^n)^m = a^(n*m), we can simplify further:
Cube root of -343 = (-7)^(3*(1/3))
Since multiplying a number by 1/3 is the same as finding its cube root, we have:
Cube root of -343 = -7
Therefore, the cube root of -343 is -7.