Find each root. √(-12)²

Verified step by step guidance

1. insert step 1> Start by understanding the expression \( \sqrt{(-12)^2} \). This involves taking the square root of a squared number.
2. insert step 2> Recognize that squaring a number and then taking the square root are inverse operations.
3. insert step 3> Simplify \((-12)^2\) first. When you square \(-12\), you multiply \(-12\) by itself, resulting in a positive number.
4. insert step 4> After squaring, you have \(144\). Now, take the square root of \(144\).
5. insert step 5> The square root of \(144\) is \(12\), since \(12 \times 12 = 144\).

Key Concepts

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the expression involves the square root of a negative number, which leads to complex numbers. The square root of a negative number can be expressed using the imaginary unit 'i', where i = √(-1).

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i'. Understanding complex numbers is essential when dealing with square roots of negative values, as they extend the number system to include solutions that are not found within the real numbers.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In the expression (-12)², the base is -12 and the exponent is 2, indicating that -12 is multiplied by itself. This operation results in a positive number, as squaring any real number, whether positive or negative, yields a non-negative result.