Question

subject: math
class: ss1 time
instruction: answer all que

1. which of the following is a surd?

a. \\(\sqrt{4}\\)
b. \\(\sqrt{9}\\)
c. \\(\sqrt{7}\\)
d. \\(\sqrt{16}\\)

1. simplify \\(\sqrt{45}\\).

a. \\(3\sqrt{5}\\)
b. \\(5\sqrt{3}\\)
c. \\(9\sqrt{2}\\)
d. \\(2\sqrt{5}\\)

1. what is the conjugate of \\(\sqrt{2} - \sqrt{5}\\)?

a. \\(\sqrt{2} + \sqrt{5}\\)
b. \\(2\sqrt{2} - \sqrt{5}\\)
c. \\(\sqrt{5} - \sqrt{2}\\)
d. \\(\sqrt{5} + \sqrt{2}\\)

1. simplify \\(\sqrt{32} + 3\sqrt{8}\\).

a. \\(10\sqrt{2}\\)
b. \\(5\sqrt{2}\\)
c. \\(8\sqrt{3}\\)
d. \\(12\sqrt{3}\\)

1. evaluate \\((2\sqrt{3} - \sqrt{5})(2\sqrt{3} + \sqrt{5})\\).

a. 7

Explanation:

Identify the surd in Question 1

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Simplify the radical in Question 2

$$ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} $$

Find the conjugate in Question 3

$$ \text{Conjugate of } (\sqrt{2} - \sqrt{5}) = \sqrt{2} + \sqrt{5} $$

Simplify the sum in Question 4

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Evaluate the product in Question 5

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$$

Answer:

Question 1

• A. \(\sqrt{4}\)
• B. \(\sqrt{9}\)
• C. \(\sqrt{7}\) (Correct answer)
• D. \(\sqrt{16}\)

Question 2

• A. \(3\sqrt{5}\) (Correct answer)
• B. \(5\sqrt{3}\)
• C. \(9\sqrt{2}\)
• D. \(2\sqrt{5}\)

Question 3

• A. \(\sqrt{2} + \sqrt{5}\) (Correct answer)
• B. \(2\sqrt{2} - \sqrt{5}\)
• C. \(\sqrt{5} - \sqrt{2}\)
• D. \(\sqrt{5} + \sqrt{2}\)

Question 4

• A. \(10\sqrt{2}\) (Correct answer)
• B. \(5\sqrt{2}\)
• C. \(8\sqrt{3}\)
• D. \(12\sqrt{3}\)

Question 5

• A. 7 (Correct answer)