RADICALS

1. Review all definitions in Radicals, also the methods of transforming and simplifying radicals. When is a radical in its simplest form?

2. Simplify (to simplest form):

3. Reduce to entire surds:

4. Reduce to radicals of lower order (or simplify indices):

5. Reduce to radicals of the same degree (order, or index): and and and and and

6. Which is greater, or ? or ?

7. Which is greatest, or ? Give work and arrange in descending order of magnitude.

Collect:

8.

9.

10.

11. A and B each shoot thirty arrows at a target. B makes twice as many hits as A, and A makes three times as many misses as B. Find the number of hits and misses of each. (Univ. of Cal.)

Reference: The chapter on Radicals in any algebra (first part of the chapter).

The most important principle in Radicals is the following:

Hence Or,

From this also

Multiply:

1. by

2. by

3. by

4. by

5. by

6. by

Divide:

7. by

8. by

9. by

10. by

11. by (Short division.)

12. by

Rationalize the denominator:

13.

14.

15.

Review the method of finding the square root of a binomial surd. (By inspection preferably.) Then find square root of:

16.

17.

18.

Reference: The chapter on Radicals in any algebra, beginning at Addition and Subtraction of Radicals.