# 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.