# Algebra - Radicals - Practice Problems

1. Rewrite with rational exponents

2. Simplify by factoring

3. In the right triangle, find the length of the side not given. Give an exact answer and an approximation to three decimal places

What is the exact value of c, what is the value of c approximated to three decimal places?

4. Multiply and simplify by factoring

5. Simplify

6. Use the laws of exponents to simplify

7. Use rational exponents to simplify. Write the answer in radical notation if possible

8. Solve

The solution is y =

9. Subtract. Simplify by collecting like terms if possible, assuming that all expressions under radicals represent non-negative numbers.

10. Multiply

11. Multiply

12. Divide. Then simplify by taking roots if possible

13. Multiply

14. Multiply

15. Add. Simplify by collecting like radical terms if possible =

16. Simplify

17. The formula can be used to approximate the speed , in miles per hour, of a car that has left skid marks of length in feet. How far will the car skid at 30 mph?

18. Find the following. Assume that can represent any real number. Use absolute value notation when necessary.

19. Solve

The solution is x =

20. Television sets. What does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 35-in TV set also has a width of 28 inches. What is its height?

21. Add. Simplify by collecting like terms, if possible. Assume that all expressions under radicals represent non-negative numbers.

22. Use rational exponents to write as a single radical expression.

23. Simplify by taking roots of the numerator and denominator.

24. Find the following. Assume that and can represent any real number.

25. What is the Pythagorean Theorem? How is it used?

[See the attached questions file]

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#### Solution Summary

Very neat and step-wise solutions are provided.

A number of algebra practice questions and solutions

Evaluate.

((-1)2 - 3)3 + 5 · (-5)

Simplify the following expression:

When converting from Fahrenheit degrees to Celsius degrees , a well known formula is used:

. Solve for .

Simplify.

Simplify.

Simplify.

Write your answer without parentheses.

Rewrite the following without an exponent.

Simplify.

Write your answer without using negative exponents.

Simplify.

3w2w-2 · 4v-9v · 2x-8x8

Use only positive exponents in your answer.

Simplify.

Multiply.

Simplify your answer as much as possible.

Multiply.

Simplify your answer.

Rewrite without parentheses and simplify.

Multiply.

Simplify your answer.

Factor

.

Factor.

Factor.

Factor:

Factor:

.

Multiply. Write your answer in lowest terms.

Simplify.

21n4/3x4y2 / 7mn2/9x3y

Subtract. Write your answer in lowest terms.

Add and simplify:

Simplify.

Solve for :

.

Simplify your answer as much as possible.

Solve for .

Solve the following proportion for .

Round your answer to the nearest tenth.

Milan runs miles in minutes. At the same rate, how many miles would he run in minutes?

Rewrite the following in simplified radical form.

Assume that all variables represent positive real numbers.

Simplify as much as possible.

Assume that all variables represent positive real numbers.

Simplify.

Assume that all variables represent positive real numbers.

Rationalize the denominator and simplify.

Solve for , where is a real number.

Solve for , where is a real number.

Find the value of .

Write the following in simplified radical form.

Solve for .

Solve the equation

for .

Solve , where is a real number.

Simplify your answer as much as possible.

Use the quadratic formula to solve for .

Write in simplified radical form by rationalizing the denominator.

Simplify.

Assume that all variables represent positive real numbers.

Multiply.

Simplify your answer as much as possible.

Simplify as much as possible.

Assume that all variables represent positive real numbers.

Simplify.

Use the quadratic formula to solve for .

Solve for .

Simplify.

Write your answer without parentheses.

Rewrite the following without an exponent.

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