key term - Square Root

Definition

The square root, denoted by the symbol √, is a mathematical operation that represents the inverse of squaring. It is used to find the value that, when multiplied by itself, results in the original number. The square root of a number is the value that, when raised to the power of 2, equals the original number.

5 Must Know Facts For Your Next Test

1. The square root symbol √ is used to indicate the inverse operation of squaring a number.
2. Simplifying expressions with square roots involves identifying perfect squares and using the properties of radicals.
3. Dividing radical expressions requires finding a common radicand and applying the laws of exponents.
4. Solving radical equations involves isolating the radical term and using the properties of square roots to find the solution.
5. Radicals can be used in functions to represent non-linear relationships, such as in the equation of a parabola.

Review Questions

• Explain how the square root operation is used in the general strategy for factoring polynomials.
  • The square root operation is an important tool in the general strategy for factoring polynomials. When a polynomial contains a perfect square term, such as $x^2$ or $4x^2$, the square root can be used to identify the factors of that term. By taking the square root of the coefficient or variable, you can determine the two factors that, when multiplied together, result in the original term. This factorization can then be used to simplify the polynomial and make it easier to solve.
• Describe the process of simplifying expressions with square roots, and how it relates to the properties of radicals.
  • Simplifying expressions with square roots involves applying the properties of radicals. This includes identifying perfect squares within the radicand, which can be simplified by taking the square root of the coefficient and the variable. Additionally, the laws of exponents, such as $\sqrt{a^2} = a$ and $\sqrt{ab} = \sqrt{a}\sqrt{b}$, can be used to simplify more complex radical expressions. Understanding these properties and how to apply them is crucial for simplifying expressions with square roots.
• Explain how square roots are used to solve radical equations, and how this process relates to the use of radicals in functions.
  • Solving radical equations involves isolating the radical term and using the properties of square roots to find the solution. This process is similar to solving other types of equations, but the presence of the square root introduces additional steps and considerations. The solutions to radical equations can then be used in functions that involve radicals, such as the equation of a parabola, which includes a square root term. Understanding how to work with square roots in both solving equations and representing functions is essential for successfully applying radicals in a variety of mathematical contexts.

Related terms

Radical:

A radical is the symbol √ used to represent the square root operation. It indicates that the value inside the radical needs to be evaluated by finding the number that, when multiplied by itself, results in the given value.

Radicand:

The radicand is the value inside the radical sign √. It is the number or expression that is being evaluated to find its square root.

Perfect Square:

A perfect square is a number that can be expressed as the product of two equal integers. For example, 4, 9, and 16 are perfect squares because they can be written as 2^2, 3^2, and 4^2, respectively.