A(2square root of 14, 5square root of7) and B(-3square root of 14, 10square root of 7)

Question

A. Consider the points A(2square root 14,5 square root7) and B(-3square root14,10square root7)

1. Write an expression that represents the slope of the line containing points A and B. Do not simplefy yet.

2. Simplify the numerator and the denominator in the expression from problem #1 by combining like radicals.

3. Write the fraction from problem #2 as the square of a fraction in lowest terms.

4. Rationalize the denominator of the expression found in problem #3.

5. Based on your answer in problem #4, does the line AB rise or fall from left to right? Explain.

B.

1. Wrtite square root2 and cube root2 using fractional exponents

2. Write the product square root2 and cube root2 using the expressions found in problem #1.

3. What is the least common denominator of the fractional exponents in problem #2?

4. Repeat problem #2 but write the fractional exponents with the common denominator from problem #3.

5. Use the rule fro multiplying exponential expression with like bases to simplify the product in problem #4 (Hint: the base remains the same, do not multiply the two bases)

6. Write the answer obtained in problem #5 as radical.

Answer 1

(A)

1) Slope of AB=(10-5)√7/[(-3-2)√14]

2) 5√7/(-5√14)

3) -√(7/14)=-√½

4) -√2/2

5) A negative slope means AB slopes downwards from left to right. As x increases y decreases at a constant rate.

(B)

1) 2^½ and 2^⅓

2), 3), 4), 5) 2=2^½+⅓ (rule for multiplying common base is to add the exponents)=2^⅚ (lowest common denominator is 6, ½=3/6 and ⅓=2/6 so their sum is 5/6).

6) 2^⅚ is the sixth root of 2⁵, which means the sixth root of 32=⁶√32.