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The value of \( \Large\sqrt{5+2\sqrt{6}} \)-\( \Large \frac{1}{\sqrt{5+2\sqrt{6}}} \) is:

A) \( \Large 2\sqrt{2} \)
B) \( \Large 2\sqrt{3} \)
C) \( \Large 1+\sqrt{5} \)
D) \( \Large \sqrt{5}-1\)

Correct Answer:

A) \( \Large 2\sqrt{2} \)

Description for Correct answer:
\( \Large \sqrt{5+2\sqrt{6}}-\frac{1}{\sqrt{5+2\sqrt{6}}} \)

=\( \Large \left(\sqrt{3}+\sqrt{2}\right)-\frac{1}{\sqrt{3}+\sqrt{2}} \)

\( \Large \left[\sqrt{5+2\sqrt{6}}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^{2} } =\sqrt{3}+\sqrt{2}\right] \)

\( \Large a^{2}+b^{2}+2ab= \left(a+b\right)^{2} \)

=\( \Large\sqrt{3}+\sqrt{2}- \left(\frac{1}{\sqrt{3}+\sqrt{2}} \times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\right)\)

=\( \Large \sqrt{3}+\sqrt{2}- \left(\frac{\sqrt{3}-\sqrt{2}}{3-2}\right) \)

=\( \Large \sqrt{3} +\sqrt{2}-\sqrt{3}+\sqrt{2}\)

=\( \Large 2\sqrt{2} \)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

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B). 16

C). 18

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B). \( \Large \sqrt[3]{24} \)

C). \( \Large 6\sqrt[3]{4} \)

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3). Simplify: \( \Large \left[ \frac{\frac{3}{2+\sqrt{3}}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}} \right]\)

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B). \( \Large 2-5\sqrt{3} \)

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4). The value of \( \Large \left(243\right) ^{0.16} \times \left(243\right)^{0.04} \) is equal to:

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5). The value of \( \Large \left(256\right) ^{0.16} \times \left(256\right)^{0.09} \) is:

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7). Simplify \( \Large \frac{0.05 \times 0.05 \times 0.05-0.04 \times 0.04 \times 0.04}{0.05 \times 0.05+0.002+0.04 \times 0.04} \)

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8). Simplify \( \Large \frac{5.32 \times 56+5.32 \times 44 }{ \left(7.66^{2}\right)- \left(2.34\right)^{2} } \)

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9). Which one of the following is least?\( \Large \sqrt{3},\sqrt[3]{2},\sqrt{2},\sqrt[3]{4} \)

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

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D). \( \Large \sqrt[3]{4} \)

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B). \( \Large \sqrt[4]{6} \)

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D). \( \Large \sqrt[12]{245} \)