Surds-quiz

\(\text{Simplify the surd: } \sqrt{50}\)

A. \(2\sqrt{5}\)

B. \(25\sqrt{2}\)

C. \(5\sqrt{2}\)

D. \(7\sqrt{2}\)

\(\text{Simplify the surd: } \sqrt{18}\)

A. \(9\sqrt{2}\)

B. \(6\sqrt{3}\)

C. \(2\sqrt{9}\)

D. \(3\sqrt{2}\)

Perform the operation: \( 2\sqrt{3} + 4\sqrt{3}\)

A. \(6\sqrt{2}\)

B. \(6\sqrt{3}\)

C. \(2\sqrt{6}\)

D. \(8\sqrt{3}\)

\(\text{Rationalize the denominator: } \frac{3}{\sqrt{5}}\)

A. \(\frac{15}{\sqrt{5}}\)

B. \(\frac{3\sqrt{5}}{10}\)

C. \(\frac{6}{5}\)

D. \(\frac{3\sqrt{5}}{5}\)

\(\text{Simplify: } 5\sqrt{8} - 3\sqrt{2}\)

A. \(8\sqrt{2}\)

B. \(7\sqrt{2}\)

C. \(10\sqrt{2}\)

D. \(2\sqrt{6}\)

\(\text{Simplify the surd: } \sqrt{27}\)

A. \(6\sqrt{3}\)

B. \(9\sqrt{3}\)

C. \(3\sqrt{3}\)

D. \(3\sqrt{9}\)

\(\text{Simplify the surd: } \sqrt{32}\)

A. \(5\sqrt{2}\)

B. \(16\sqrt{2}\)

C. \(4\sqrt{2}\)

D. \(2\sqrt{8}\)

Perform the operation:

\( 5\sqrt{5} + 7\sqrt{5}\)

A. \(35\sqrt{5}\)

B. \(12\sqrt{5}\)

C. \(2\sqrt{10}\)

D. \(5\sqrt{7}\)

\(\text{Rationalize the denominator: } \frac{4}{\sqrt{7}}\)

A. \(\frac{28}{\sqrt{7}}\)

B. \(\frac{4\sqrt{7}}{49}\)

C. \(\frac{4\sqrt{7}}{7}\)

D. \(\frac{8}{7}\)

\(\text{Simplify: } 3\sqrt{12} - 2\sqrt{3}\)

A. \(5\sqrt{3}\)

B. \(6\sqrt{3}\)

C. \(4\sqrt{3}\)

D. \(1\sqrt{3}\)

\(\text{Perform the operation: } 6\sqrt{7} - 3\sqrt{7}\)

A. \(3\sqrt{7}\)

B. \(18\sqrt{7}\)

C. \(9\sqrt{7}\)

D. \(2\sqrt{14}\)

\(\text{Rationalize the denominator: } \frac{5}{\sqrt{3}}\)

A. \(\frac{5\sqrt{3}}{9}\)

B. \(\frac{15}{\sqrt{3}}\)

C. \(\frac{5\sqrt{3}}{3}\)

D. \(\frac{10}{3}\)

\(\text{Simplify: } 7\sqrt{28} + 4\sqrt{7}\)

A. \(18\sqrt{7}\)

B. \(15\sqrt{7}\)

C. \(11\sqrt{7}\)

D. \(7\sqrt{4}\)

\(\text{Simplify the surd: } \sqrt{45}\)

A. \(5\sqrt{9}\)

B. \(9\sqrt{5}\)

C. \(3\sqrt{5}\)

D. \(7\sqrt{5}\)

Expand and simplify: \(\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)\)

A. \(5\sqrt{3}\)

B. 14

C. \(6\sqrt{5}\)

D. 4

\(\text{Evaluate: } \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\)

A. \(2-\sqrt{3}\)

B. \(2\sqrt{3}\)

C. \(5- 2\sqrt{3}\)

D. 1

\(\text{Evaluate: } \left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)\)

A. \(4\sqrt{7}\)

B. 9

C. 8

D. \(16 - \sqrt{7}\)

\(\text{Evaluate: } \left(5+\sqrt{2}\right)\left(5-\sqrt{2}\right)\)

A. \(10\)

B. \(23\)

C. \(27\)

D. \(5\sqrt{2}\)

\(\text{Evaluate: } \left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right)\)

A. \(3\sqrt{11}\)

B. \(9\sqrt{11}\)

C. \(- 2\)

D. \(6\)

\(\text{Evaluate: } \left(6+\sqrt{13}\right)\left(6-\sqrt{13}\right)\)

A. \(12\)

B. \(6+\sqrt{13}\)

C. \(6\sqrt{13}\)

D. \(23\)

\(\text{Evaluate: } \frac{\sqrt{5}}{7-\sqrt{3}}\)

A. \(\frac{15\sqrt{5}}{46} - \frac{9\sqrt{15}}{46}\)

B. \(\frac{17\sqrt{5}}{11} + \frac{7\sqrt{15}}{11}\)

C. \(\frac{\left(7\sqrt{5}-\sqrt{15}\right)}{46}\)

D. \(\frac{\left(7\sqrt{5}+\sqrt{15}\right)}{46}\)

\(\text{Evaluate: } \frac{3+\sqrt{6}}{\sqrt{4}-\sqrt{2}}\)

A. \(4 + \sqrt{12} - \sqrt{6}\)

B. \(5 - \sqrt{12} + \sqrt{6}\)

C. \(\frac{1}{2}\left(3\sqrt{2}+2\sqrt{3}+2\sqrt{6}\right)\)

D. \(6 + \sqrt{12} + \sqrt{6}\)

\(\text{Evaluate: } \frac{6\sqrt{5}}{5-\sqrt{3}}\)

A. \(\frac{13\sqrt{5}}{11} + \frac{9\sqrt{15}}{11}\)

B. \(\frac{17\sqrt{5}}{11} + \frac{7\sqrt{15}}{11}\)

C. \(\frac{15\sqrt{5}}{11} - \frac{9\sqrt{15}}{11}\)

D. \(\frac{15\sqrt{5}}{11} + \frac{3\sqrt{15}}{11}\)

\({\text{Evaluate: } \frac{7\sqrt{2}}{4-\sqrt{3}}}\)

A. \(\frac{27\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\)

B. \(\frac{28\sqrt{2}}{13} - \frac{21\sqrt{6}}{13}\)

C. \(\frac{28\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\)

D. \(\frac{26\sqrt{2}}{13} + \frac{20\sqrt{6}}{13}\)

\(Simplify: \sqrt{250}\)

A. \(5\sqrt{10}\)

B. 50

C. 25

D. 10

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