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Multiplying Radical Expressions Worksheets These Radical Worksheets will produce problems for multiplying radical expressions. You may select the difficulty for each expression.

Simplifying Radical Expressions

Dividing Radical Expressions Worksheets These Radical Worksheets will produce problems for dividing radical expressions. You may select the difficulty for each problem. Scientific Notation Worksheets These Scientific Notation Worksheets will produce problems for practicing how to read and write numbers in standard form and scientific notation.

You may select problems with multiplication, division, or products to a power. These worksheets produces 12 problems per page. These Scientific Notation Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Operations with Perfect Squares and Cubes Worksheets These Exponents and Radicals Worksheets will produce problems for finding the squares and cubes of positive integers, as well as the square and cube root of perfect squares and perfect cubes. These worksheets produce 18 problems per page. These Exponents and Radicals Worksheets are a good resource for students in the 5th Grade through the 8th Grade.


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Algebraic Operations with Perfect Squares and Cubes Worksheets These Exponents and Radicals Worksheets will produce problems for finding the squares and cubes of algebraic variables, as well as the square and cube root of variables. Worksheets By Topics. Exponents Properties Handout.

Simplifying radical expressions (addition)

Square Roots Chart Handout. Simple Exponent Worksheets. Integers with Exponent Worksheets. Fractions with Exponent Worksheets. Exponents with Multiplication Worksheets. Exponents with Division Worksheets.

Radicals (miscellaneous videos)

Powers of Products Exponents Worksheets. Powers of Quotients Exponents Worksheets. Powers of Products and Quotients Worksheets. Evaluating Exponential Functions Worksheets. Operations with Exponents Worksheets. Simplifying Radicals Worksheets. Simplifying Radical Expressions Worksheets. Adding and Subtracting Radical Expressions. Solution: Begin by determining the square factors of 18, x 3 , and y 4. Make these substitutions and then apply the product rule for radicals and simplify. Example 4: Simplify: 4 a 5 b 6. Solution: Begin by determining the square factors of 4, a 5 , and b 6.

Example 5: Simplify: 80 x 5 y 7 3. Solution: Begin by determining the cubic factors of 80, x 5 , and y 7. Example 6: Simplify 9 x 6 y 3 z 9 3. It will be left as the only remaining radicand because all of the other factors are cubes, as illustrated below:. Replace the variables with these equivalents, apply the product and quotient rule for radicals, and then simplify. Example 7: Simplify: 81 a 4 b 5 4. Solution: Determine all factors that can be written as perfect powers of 4.

Hence the factor b will be left inside the radical. Solution: Notice that the variable factor x cannot be written as a power of 5 and thus will be left inside the radical.

Formulas Involving Radicals

Try this! Simplify: x 6 y 7 z Assume all variables are positive. To easily simplify an n th root, we can divide the powers by the index. If the index does not divide into the power evenly, then we can use the quotient and remainder to simplify. For example,. The quotient is the exponent of the factor outside of the radical, and the remainder is the exponent of the factor left inside the radical. We next review the distance formula. The distance, d , between them is given by the following formula:. Recall that this formula was derived from the Pythagorean theorem.

Simplifying Radicals With Variables, Exponents, Fractions, Cube Roots - Algebra

Solution: Use the distance formula with the following points. It is a good practice to include the formula in its general form before substituting values for the variables; this improves readability and reduces the probability of making errors. Answer: 6 2 units. Example The period, T , of a pendulum in seconds is given by the formula. If the length of a pendulum measures 6 feet, then calculate the period rounded off to the nearest tenth of a second.

Solution: Substitute 6 for L and then simplify. Answer: The period is approximately 2. We know that the square root is not a real number when the radicand x is negative. Therefore, we conclude that the domain consists of all real numbers greater than or equal to 0. Here we choose 0 and some positive values for x , calculate the corresponding y -values, and plot the resulting ordered pairs.

After plotting the points, we can then sketch the graph of the square root function. Solution: Replace x with each of the given values. Since the cube root could be either negative or positive, we conclude that the domain consists of all real numbers. For completeness, choose some positive and negative values for x , as well as 0, and then calculate the corresponding y -values. Plot the points and sketch the graph of the cube root function. Assume all variables represent positive numbers.

Rewrite the following as a radical expression with coefficient 1. Assume that the variable could represent any real number and then simplify. Find the y -intercepts for the following. Use the distance formula to calculate the distance between the given two points.