# The Equivalent

Radicals and fractional exponents are alternate ways of expressing the same thing. In the table below we show equivalent ways to express radicals: with a root, with a rational exponent, and as a principal root. Let’s look at some more examples, but this time with cube roots. Remember, cubing a number raises it to the power of three.

DEFINITION Radical expressions are said to be similar when they have the same radical index and the same radicand. EXAMPLES 1. The redical expressions 3 √2 and 5 √2 are similar.

## How do you write a radical expression?

A radical expression is said to be in standard form if the following conditions hold:

2. The radical index is as small as possible.
3. The exponent of each factor of the radicand is a natural number less than the radical index.
4. There are no fractions in the radicand.
5. There are no radicals in the denominator of a fraction.

The definition of a radical expression is any mathematical expression which uses a root symbol – a square root, cube root, 4th root, etc. The value (s) underneath the radical sign itself is known as the radicand, the the small number to the left is called the degree. If there is no degree, it’s simply a square root. What is the radical of 7?

## What are the parts of a radical expression?

Parts of a Radical Expression. A radical expression has three parts or components: the radical symbol, the radicand, and the index or degree of the radical. The radical symbol or radical sign is the symbol that indicates we are taking the root of a number. In this case, we are seeing the radical symbol with a 3 written on the left side.

## What is the definition of radical expression?

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a ‘square root’ symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher.

## How do you find equivalent radical expressions?

0:042:56Radical equivalent to rational exponents | Algebra I | Khan AcademyYouTubeStart of suggested clipEnd of suggested clipThis is the same thing as d. Times the principal root of four times the principal root of d to theMoreThis is the same thing as d. Times the principal root of four times the principal root of d to the fourth.

## What is an example of a radical expression?

Some examples of radical expressions include √2,3√72,√2x+7, and 4√1p. 2 , 72 3 , 2 x + 7 , and 1 p 4 .

## What is a equivalent expression?

What are equivalent expressions? Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

## How do you write a radical expression?

0:002:33Write Expressions Using Radicals and Rational Exponents – YouTubeYouTubeStart of suggested clipEnd of suggested clipExample we’re asked to write each radical expression using rational exponents looking at the notes.MoreExample we’re asked to write each radical expression using rational exponents looking at the notes. We’re given the square root of x equals x to the one half.

## What are the 3 parts of a radical expression?

The radical expression ab has three major features, the radical symbol (it looks like a check mark), the index (the small number tucked outside the radical symbol), and the radicand, the quantity written beneath the horizontal bar of the radical symbol.

## What are examples of equivalent expressions?

Examples of Equivalent Expressions 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x2 + 2y + 1) = 6×2 + 12y + 6. In this lesson, we learn to identify equivalent expressions.

## How do you write an equivalent expression?

You can write equivalent expressions by combining like terms. Like terms are terms that have the same variables raised to the same powers. For example, the list shows some pairs of like terms. the new coefficient is 9.

## How do you simplify an equivalent expression?

0:572:24Equivalent Expressions And Simplifying – YouTubeYouTubeStart of suggested clipEnd of suggested clipWe can combine this X – this X and this X. Which is a total of 3x. And we can combine 4 + 2 which isMoreWe can combine this X – this X and this X. Which is a total of 3x. And we can combine 4 + 2 which is a total of 6. And 3x plus 6 is not equal to 2x + 6 thereby eliminating choice C as well.

## How do you express a radical in simplest form?

0:573:44Simplest Radical Form – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo the square root of 45. And simplest radical form is three times the square root of. Five. Let’sMoreSo the square root of 45. And simplest radical form is three times the square root of. Five. Let’s try another example. Once again we are going to start by breaking 180. Down into two factors.

## How do you find the radical equation?

To solve a radical equation:Isolate the radical expression involving the variable. … Raise both sides of the equation to the index of the radical.If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

## How do I simplify radicals?

To simplify a radical expression, simplify any perfect squares or cubes, fractional exponents, or negative exponents, and combine any like terms that result. If there are fractions in the expression, split them into the square root of the numerator and square root of the denominator.

## Which of the following is an example of radical equation?

Explanation: Examples of radicals are: √46 and ³√81 . A radical equation is an equation that comprises one or more radicals.

## How do you identify a radical?

0:282:30What is the identify element of a radical expression – YouTubeYouTubeStart of suggested clipEnd of suggested clipWhen you have the nth root of your of a number raised to the nth. Power. Then that just equals.MoreWhen you have the nth root of your of a number raised to the nth. Power. Then that just equals.

## How do you simplify radicals examples?

2:566:18Simplifying radicals examples – YouTubeYouTubeStart of suggested clipEnd of suggested clipPower is going to be equal to 180 times one-half to the one-half. Power taking the square root theMorePower is going to be equal to 180 times one-half to the one-half. Power taking the square root the principal root is the same thing as raising something to the one-half.

## How can you tell that an equation is a radical equation or not?

A radical equation is an equation in which a variable is under a radical. To solve a radical equation: Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Radical expressions are expressions that contain radicals. Radical expressions come in many forms, from simple and familiar, such as √16 16, to quite complicated, as in 3√250x4y 250 x 4 y 3.

## How to simplify radical expressions?

Simplify radical expressions using rational exponents and the laws of exponents. An alternative method to factoring is to rewrite the expression with rational exponents, then use the rules of exponents to simplify. You may find that you prefer one method over the other. Either way, it is nice to have options.

## What is the exponent of 1 2 1 2?

So, an exponent of 1 2 1 2 translates to the square root, an exponent of 1 5 1 5 translates to the fifth root or 5√ 5, and 1 8 1 8 translates to the eighth root or 8√ 8. Express (2x)1 3 ( 2 x) 1 3 in radical form. Rewrite the expression with the fractional exponent as a radical.

## Why use rational exponents?

They may be hard to get used to, but rational exponents can actually help simplify some problems. Writing radicals with rational exponents will come in handy when we discuss techniques for simplifying more complex radical expressions. Radical expressions are expressions that contain radicals.

## What is the denominator of the rational exponent?

Remember, cubing a number raises it to the power of three. Notice that in the examples in the table below, the denominator of the rational exponent is the number 3.

Rewrite the radical using a rational exponent. The root determines the fraction. In this case, the index of the radical is 3, so the rational exponent will be 1 3 1 3.

## What is square root?

Square roots are most often written using a radical sign, like this, √4 4. But there is another way to represent them. You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. For example, √4 4 can be written as 41 2 4 1 2.

## When are radical expressions said to be similar?

DEFINITION Radical expressions are said to be similar when they have the same radical index and the same radicand.

## How to find the radical value?

The value of the radical is obtained by forming the product of the factors. where the exponent of each factor is its original exponent divided by the radical index.

## When do radical index and exponents of all the factors in the radicand have a common factor?

When the radical index and the exponents of all the factors in the radicand have a common factor, divide both the radical index and the exponents of the factors of the radicand by their common factor That is, apply nk√amk=n√am to obtain the smallest possible radical index.

## What is the nth power of 2,a,32, and b3?

The nth powers of 2,a,32, and b3 are, respectively, 2 2n,an,32 n, and b3 n.#N#When n is an even number, the nth power of a positive or a negative number is a positive number. For example,

## How is radical index 2 distributed?

In our example, the radical index 2 is distributed over each factor of 2 4 · x 2 · x y.

## What is the prime number 2 to the power of 4?

Prime number 2 to the power of 4 equals 16.

## What is the index of a radical?

The n in n√a (always a natural number greater than 1) is called the index or the order of the radical, and a is called the radicand. When there is no indicated index, as in √a, the index 2 is implied and it is read “the square root of a .” When the index is 3 as in 3√a, it is read “the cube root of a .”