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Surds and indices Practice Questions & Answers

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The value of $\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4...........}}}}}}$ is :

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The value of $\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4...........}}}}}}$ is :
1). 2
2). $2^{2}$
3). $2^{3}$
4). $2^{5}$

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$\sqrt{30+\sqrt{30+\sqrt{30+.....}}}$ is equal to

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$\sqrt{30+\sqrt{30+\sqrt{30+.....}}}$ is equal to
1). 5
2). $3\sqrt{10}$
3). 6
4). 7

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$\sqrt{3\sqrt{3\sqrt{3.....}}}$ is equal to

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$\sqrt{3\sqrt{3\sqrt{3.....}}}$ is equal to
1). $\sqrt{3}$
2). 3
3). $2\sqrt{3}$
4). $3\sqrt{3}$

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$\sqrt{6+\sqrt{6+\sqrt{6+.....}}}$ is equal to

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$\sqrt{6+\sqrt{6+\sqrt{6+.....}}}$ is equal to
1). 3
2). 4
3). 5
4). 6

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$\sqrt{12+\sqrt{12+\sqrt{12+.....}}}$ is equal to

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$\sqrt{12+\sqrt{12+\sqrt{12+.....}}}$ is equal to
1). 3
2). 4
3). 6
4). 2