Perfect Square Roots Math Problems

Perfect Squares

• A perfect square is a number that can be expressed as the square of an integer (e.g., 36 = 6 × 6)
• The square root of a perfect square is always a whole number (e.g., √36 = 6)

Method for Finding Square Roots

• The method involves subtracting consecutive odd numbers from the number until the result reaches 0
• The number of subtractions performed is equal to the square root of the given number
• This method is only applicable to perfect square numbers

Square and Cube Roots

• The square root of a number is the value that, when multiplied by itself, equals the original number (e.g., √4 = √(2 × 2) = 2)
• The cube root of a number is the value that, when multiplied by itself three times, equals the original number (e.g., ∛27 = ∛(3 × 3 × 3) = 3)

Key Properties

• The square root of a negative number cannot be negative
• The cube root of a negative number can be negative

General Method for Finding Roots

• To find the square root of a number, find a number that, when multiplied by itself, equals the original number
• To find the cube root of a number, find a number that, when multiplied by itself three times, equals the original number

Absolute Value

• Absolute value is a positive value that shows how far a number is from zero on the number line.
• It is always positive, regardless of whether the number is positive or negative.
• Example: the absolute value of -5 is 5, because it is 5 units away from zero on the number line.

Solving Absolute Value Equations

• To solve an absolute value equation, write two equations: one with a positive value and one with a negative value.
• Example: |x + 2| = 9 can be solved by writing two equations: x + 2 = 9 and x + 2 = -9.
• Solve for x in both equations to get two solutions.

Polynomials

• A polynomial is a math phrase with terms that have numbers and letters.
• Each term is called a monomial, and they can be combined by adding or subtracting.
• Example: (6k - 7k²) + (4k² + 6) = -3k² + 6k + 6.

Solving Polynomial Equations

• To solve a polynomial equation, write it in standard form.
• When the equation is equal to zero, factor it and then set each variable factor equal to zero.
• The solutions to the resulting equations are the solutions to the original equation.
• Not all polynomial equations can be solved by factoring.