# Several problems on Radical expressions

Radical Expressions. See attachment for equations

1. Find the square root of 8100

2. Find the square root that is the real number

3. Find each function value, if it exists

4. Find the following. Assume that variables can represent any real number.

5. Rewrite without exponents =

6. Rewrite with rational exponents

7. Simplify the expression

8. Use the laws of exponents to simplify

9. Rewrite using only positive rational exponents.

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

11. Simplify by factoring. = type an exact answer, using radicals as needed.

12. Simplify by factoring. =

13. Multiply and simplify. Assume that all expressions under the radicals represent nonnegative numbers. =

14. Multiply and simplify by factoring. Assume that all expressions under the radicals represent nonnegative numbers. =

15. Simplify by factoring. Assume that all expressions under the radicals represent nonnegative numbers. =

16. Simplify by factoring. Assume that all expressions under the radicals represent nonnegative numbers. =

17. Multiply and simplify by factoring. Assume that all expressions under the radicals represent nonnegative numbers. =

18. Divide then simplify by taking roots, if possible. Assume that all expressions under radicals represent positive numbers. =

19. Divide then simplify by taking roots, if possible. Assume that all expressions under radicals represent positive numbers. =

20. Divide and simplify. Assume that all expressions under radicals represent nonnegative numbers. =

21. Simplify by taking roots of the numerator and the denominator. Assume that all expressions under radicals represent positive numbers. =

22. Add or subtract. Simplify by collecting like radical terms, if possible.
- + =

23. Add. Simplify by collecting like radical terms, if possible. + =

24. Add. Simplify by collecting like radical terms, if possible, assuming that all expressions under radicals represent nonnegative numbers. + =

25. Multiply. =

26. Multiply. =

27. Rationalize the denominator. =

28. Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. =

29. Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. =

30. Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. =

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Extracted Content from Question Files:

1. Find the square root of 8100

− 49
2. Find the square root that is the real number

f (t ) = t 2 + 1
3. Find each function value, if it exists
f (0) =

4. Find the following. Assume that variables can represent any real number.

(a + 4)
2
=

x1 / 6 =
5. Rewrite without exponents

xy 3 z =
6. Rewrite with rational exponents 4

7. Simplify the expression 1000 −5 / 3

4 .2 5 / 4
=
8. Use the laws of exponents to simplify
4 .2 2 / 5

(x )
5 / 3 −3 / 4
=
9. Rewrite using only positive rational exponents.

x1 / 3 ⋅ y 1 / 6 ⋅ z 1 / 2 as a single radical expression.
10. Use rational exponents to write

700 x 4 = type an exact answer, using radicals as needed.
11. Simplify by factoring.

4
12. Simplify by factoring. 405 =

13. Multiply and simplify. Assume that all expressions under the radicals represent
nonnegative numbers. 7 x 14 x =

14. Multiply and simplify by factoring. Assume that all expressions under the radicals
y7 81 y 8 =
represent nonnegative numbers. 3 3
15. Simplify by factoring. Assume that all expressions under the radicals represent
162 x 4 y 6 =
nonnegative numbers. 4

16. Simplify by factoring. Assume that all expressions under the radicals represent
192 x 12 y 25 =
nonnegative numbers. 5

17. Multiply and simplify by factoring. Assume that all expressions under the radicals
3b 7 21c 8 =
represent nonnegative numbers.

18. Divide then simplify by taking roots, if possible. Assume that all expressions under
10a
5a

19. Divide then simplify by taking roots, if possible. Assume that all expressions under
3
88a 10 b 8
3
11a 8 b 7

20. Divide and simplify. Assume that all expressions under radicals represent
x3
4
nonnegative numbers. =
5
x

21. Simplify by taking roots of the numerator and the denominator. Assume that all
243 x 9
expressions under radicals represent positive numbers. =
5
y 15

22. Add or subtract. Simplify by collecting like radical terms, if possible.
6 7 -2 7 +3 7 =

23. Add. Simplify by collecting like radical terms, if possible. 6 45 + 2 125 =

24. Add. Simplify by collecting like radical terms, if possible, assuming that all
7 a + 4 63a 3 =
expressions under radicals represent nonnegative numbers.

10 5 − 4 10 =
25. Multiply.
a  3 2a 2 + 3 16a 2  =
3
 
26. Multiply.
 

15 7
27. Rationalize the denominator. =
75

28. Rationalize the denominator. Assume that all expressions under radicals represent
3y 4
3
positive numbers. =
3
6x 4

29. Rationalize the denominator. Assume that all expressions under radicals represent
3− x
positive numbers. =
5+ x

30. Rationalize the denominator. Assume that all expressions under radicals represent
c− d
positive numbers. =
c+ d