radical expression

Examples of radical expression in the following topics:

• Simplifying Radical Expressions

  • Radical expressions containing variables can be simplified to a basic expression in a similar way to those involving only integers.
  • Expressions that include roots are known as radical expressions.
  • A radical expression is said to be in simplified form if:
  • Radical expressions that contain variables are treated just as though they are integers when simplifying the expression.
  • As with numbers with rational exponents, these rules can be helpful in simplifying radical expressions with variables.

• Adding, Subtracting, and Multiplying Radical Expressions

  • An expression with roots is called a radical expression.
  • To add radicals, the radicand (the number that is under the radical) must be the same for each radical, so, a generic equation will have the form:
  • Multiplication of radicals simply requires that we multiply the variable under the radical signs.
  • For example, the radical expression $\displaystyle \sqrt{\frac{16}{3}}$ can be simplified by first removing the squared value from the numerator.
  • Explain the rules for calculating the sum, difference, and product of radical expressions

• Introduction to Radicals

  • Radical expressions yield roots and are the inverse of exponential expressions.
  • Mathematical expressions with roots are called radical expressions and can be easily recognized because they contain a radical symbol ($\sqrt{}$).
  • For example, the following is a radical expression that reverses the above solution, working backwards from 49 to its square root:
  • In this expression, the symbol is known as the "radical," and the solution of 7 is called the "root."
  • This is read as "the square root of 36" or "radical 36."

• Fractions Involving Radicals

  • In mathematics, we are often given terms in the form of fractions with radicals in the numerator and/or denominator.
  • When we are given expressions that involve radicals in the denominator, it makes it easier to evaluate the expression if we rewrite it in a way that the radical is no longer in the denominator.
  • You are given the fraction $\frac{10}{\sqrt{3}}$, and you want to simplify it by eliminating the radical from the denominator.
  • Recall that a radical multiplied by itself equals its radicand, or the value under the radical sign.
  • Therefore, multiply the top and bottom of the fraction by $\frac{\sqrt{3}}{\sqrt{3}}$, and watch how the radical expression disappears from the denominator:$\displaystyle \frac{10}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = {\frac{10\cdot\sqrt{3}}{{\sqrt{3}}^2}} = {\frac{10\sqrt{3}}{3}}$

• Imaginary Numbers

  • A radical expression represents the root of a given quantity.
  • What does it mean, then, if the value under the radical is negative, such as in $\displaystyle \sqrt{-1}$?
  • When the radicand (the value under the radical sign) is negative, the root of that value is said to be an imaginary number.

• Solving Problems with Radicals

  • Roots are written using a radical sign, and a number denoting which root to solve for.
  • Roots are written using a radical sign.
  • Any expression containing a radical is called a radical expression.
  • You want to start by getting rid of the radical.
  • Do this by treating the radical as if it where a variable.

• Domains of Rational and Radical Functions

  • Rational and radical expressions have restrictions on their domains which can be found algebraically or graphically.
  • A rational expression is one which can be written as the ratio of two polynomial functions.
  • The radicand is the number or expression underneath the radical sign.  
  • Example 3:  What is the domain of the radical function: $f(x) = \sqrt {x-3} +4$?
  • Calculate the domain of a rational or radical function by finding the values for which it is undefined

• Radical Functions

  • An expression with roots is called a radical function, there are many kinds of roots, square root and cube root being the most common.
  • An expression with roots is called a radical expression.
  • Using algebra will show that not all of these expressions are functions and that knowing when an expression is a relation or a function allows certain types of assumptions to be made.
  • The shape of the radical graph will resemble the shape of the related exponent graph it were rotated 90-degrees clockwise.
  • Discover how to graph radical functions by examining the domain of the function

• Radical Equations

  • Equations involving radicals are often solved by moving the radical to one side of the equation and then squaring both sides.
  • Steps to Solve a Radical Equation with a variable under the radical symbol
  • Suppose $a$ and $b$ are algebraic expressions.  
  • Make sure the radical is positive.
  • $(\sqrt{6x-2})^2=(10)^2$,  squaring a square root leaves the expression under the square root symbol and $10$ squared is $100$

• The Triumph of Congressional Reconstruction

  • Radical Reconstruction was a period of the Reconstruction Era during which the Radical Republicans held control of Reconstruction policies.
  • Radical Reconstruction was a period following the Civil War during which radical Republicans controlled Reconstruction policies, though they often clashed with President Johnson over pieces of legislation.
  • Radical Republicans in Congress, however, led by Stevens and Sumner, opened the way for male freedmen suffrage.
  • With the Radicals in control, Congress passed four statutes known as Reconstruction Acts on March 2, 1867.
  • Gorham, Union Party candidate for governor of California in 1867, was "...the only one that had the honesty and at the same time the imprudence to express himself opposed to the anti-Chinese movement, and had in consequence lost many votes and impaired his future political prospects...."