# How To Simplify Radical Expressions

How To Simplify Radical Expressions – This is “Simplifying Radical Expressions”, section 8.2 from the book Beginning Algebra (v. 1.0). For details about it (including licensing), click here.

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## How To Simplify Radical Expressions

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### Critical Thinking Skill: Demonstrate Understanding Of Concepts

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An algebraic expression with radicals is called a radical expressionAlgebraic expressions with radicals. . We use products and quotient rules to simplify them.

Is a variable, it can represent an arbitrary number. So we have to make sure that the result is good including a full quality driver.

Normally, at this point to begin the algebra texts note that all variables are considered positive. If so, then

In the previous example it is correct and no full value driver is needed. The example can be simplified as follows:

In this section, we will assume that all variables are positive. This enables us to concentrate on reading

Root problem. Therefore, we will use the following property for the rest of the section:

Solution: Coefficient 9=32 and therefore does not have a perfect cube factor. It will always be the only one left strong because all the other points are cubes, as shown below:

Solution: Find all the factors that can be written as perfect powers of 4. Here it is important to see that b5=b4⋅b. Therefore, the point b will remain in the radical.

Cannot be written as a power of 5 and so will remain in the radical. Furthermore, for y6=y5⋅y; point

If the index is not evenly divided by power, then we can use the quotient and the remainder to simplify. For example,

The quotient is the exponent of the factor outside the radical, and the remainder is the exponent of the factor left inside the radical.

### Simplify Radical Expressions Using The Distributive Property 1

Distance formula Given two points (x1, y1) and (x2, y2), calculate the distance d between them using the formula d = ( x 2− x 1) 2+( y 2− y 1)2 . :

It is good practice to enter a formula in its general form before entering values ​​for variables; this improves readability and reduces the chance of making mistakes.

Represents the length of the pendulum in feet. If the length of the pendulum is 6 feet, then calculate the swing time to the nearest tenth of a second.

It’s bad. So we conclude that the domain contains all real numbers greater than or equal to 0. Here we choose 0 and other positive values ​​for

Since cube roots can be negative or positive, we conclude that the square contains all real numbers. For completeness, select positive and negative values ​​of

97. The speed of a car before braking can be estimated by the length of the skid marks left on the road. In a dry, fast,

Represents the length of the slide marks in feet. Estimate the car’s speed before applying the brakes on a dry stretch of road about 36 feet.

Represents the height of the circle. What is the volume of the circle if the volume is 36π cubic centimeters?

Represents the length of the feet. Calculate the time, according to the following length. Give the exact value and the estimated value to the nearest tenth of a second.

Represents the distance it has fallen in feet. Calculate the time it takes for the object to fall, given the following distance. Give the exact value and the estimated value to the nearest tenth of a second.

121. Research and discuss the methods used to calculate square roots before the common use of electronic calculators. By using our website, you agree to our cookie policy. Cookie Settings

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#### How To Simplify Rational Exponents? (w/ 29 Examples!)

There are 10 references mentioned in this article, which can be found at the bottom of the page.

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To simplify an expression, simplify perfect squares or cubes, fractional exponents or negative exponents, and combine any like terms that appear. If there are fractions in the expression, divide them by the square root of the numerator and the square root of the denominator. If you need to extract square factors, place the imperfect factor in its original factor and subtract the perfect square multiples from the factor. For tips on setting denominators, read on!