Question

recall that the product \\((a + b)(a - b)\\) is the difference of squares, \\(a^2 - b^2\\).
examine this same product for radical expressions.

choose the product of \\((3 + \sqrt{7})(3 - \sqrt{7})\\)
\\(6 - 3\sqrt{7} + 3\sqrt{7} - \sqrt{14}\\)
\\(9 - \sqrt{21} + \sqrt{21} - \sqrt{49}\\)
\\(9 - 3\sqrt{7} + 3\sqrt{7} - \sqrt{49}\\)

simplify the product of \\((3 + \sqrt{7})(3 - \sqrt{7})\\) that you found in the previous step.
\\((3 + \sqrt{7})(3 - \sqrt{7}) = \\)

Explanation:

Expand the product using the distributive property

Using the Multiplying Binomial Radicals knowledge point

$$ (3+\sqrt{7})(3-\sqrt{7}) = 3(3) - 3\sqrt{7} + 3\sqrt{7} - \sqrt{7}\sqrt{7} $$

$$ (3+\sqrt{7})(3-\sqrt{7}) = 9 - 3\sqrt{7} + 3\sqrt{7} - \sqrt{49} $$

Simplify the expanded expression

Using the Radical Conjugates and Radical Simplification knowledge points

$$ 9 - 3\sqrt{7} + 3\sqrt{7} - \sqrt{49} = 9 - \sqrt{49} $$

$$ 9 - 7 = 2 $$

Answer:

Question 1

• (A) \(6-3\sqrt{7}+3\sqrt{7}-\sqrt{14}\)
• (B) \(9-\sqrt{21}+\sqrt{21}-\sqrt{49}\)
• (C) \(9-3\sqrt{7}+3\sqrt{7}-\sqrt{49}\) (Correct answer)

Question 2

Simplify the product of \((3+\sqrt{7})(3-\sqrt{7})\) that you found in the previous step.
\((3+\sqrt{7})(3-\sqrt{7}) =\) <blank>2</blank>