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.