1. Simplify

2. Find the prime factors of

(a)

(b)

3. (a) Simplify

3. (b) Show that

4. Define homogeneous terms.

4. For what value of n is a homogeneous binomial?

5. Extract the square root of

6. Two vessels contain each a mixture of wine and water. In the first vessel the quantity of wine is to the quantity of water as and in the second as What quantity must be taken from each, so as to form a third mixture which shall contain 5 gallons of wine and 9 gallons of water?

7. Find a quantity such that by adding it to each of the quantities a, b, c, d, we obtain four quantities in proportion.

8. What values must be given to a and b, so that may be equal?