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The value of \( \Large \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}} \) is:

A) 1
B) 2
C) 3
D) 8

Correct Answer:


B) 2

Description for Correct answer:
\( \Large \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}} \)

=\( \Large \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{4+3+2 \times 2 \times \sqrt{3}}}} \)\\

=\( \Large \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{ \left(2+\sqrt{3}\right)^{2} }}} \)

=\( \Large \sqrt{-\sqrt{3}+\sqrt{3+8 \left(2+\sqrt{3}\right) }} \)

=\( \Large \sqrt{-\sqrt{3}+\sqrt{3+16+8\sqrt{3}}} \)

=\( \Large \sqrt{\sqrt{-3}+\sqrt{ \left(\sqrt{3}\right)^{2} + \left(4\right)^{2}+2 \times 4 \times \sqrt{3} } }\)

=\( \Large \sqrt{-\sqrt{3}+\sqrt{ \left(4+\sqrt{3}\right)^{2} }} \)

=\( \Large \sqrt{-\sqrt{3}+4+\sqrt{3}} = \sqrt{4} =2\)

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

Comments

Similar Questions

1). \( \Large \sqrt{\sqrt[3]{0.004096}} \) is equal to:

A). 4

B). 0.4

C). 0.04

D). 0.004

2). The approximate value of \( \Large \frac{3\sqrt{12}}{2\sqrt{28}}\div\frac{2\sqrt{21}}{\sqrt{98}} \) is:

A). 1.0727

B). 1.0606

C). 1.6026

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3). \( \Large \frac{2.3 \times 2.3 \times 2.3-1}{2.3 \times 2.3+2.3+1} \) is equal to:

A). 1.3

B). 3.3

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4). The ascending order of \( \Large \left(2.89\right)^{0.5},2- \left(0.5\right)^{2},\sqrt{3} and \sqrt[3]{0.008} \) is:

A). \( \Large 2- \left(0.5\right)^{2},\sqrt{3},\sqrt[3]{0.008}, \left(2.89\right)^{0.5} \)

B). \( \Large \sqrt[3]{0.008}, \left(2.89\right)^{0.5},\sqrt{3}, 2- \left(0.5\right)^{2} \)

C). \( \Large \sqrt[3]{0.008},\sqrt{3},\left(2.89\right)^{0.5}, 2- \left(0.5\right)^{2} \)

D). \( \Large \sqrt{3},\sqrt[3]{0.008},2- \left(0.5\right)^{2},\left(2.89\right)^{0.5} \)

5). The greatest onr of the \( \Large \sqrt{2},\sqrt[3]{3},\sqrt[6]{6},\sqrt[5]{5} \) is:

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

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

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

D). \( \Large \sqrt[5]{5} \)

6). Given \( \Large \sqrt{2} =1.414\).The valueof \( \Large \sqrt{8} +2\sqrt{32}-3\sqrt{128}+4\sqrt{50}\) is:

A). 8.484

B). 8.526

C). 8.426

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7). If \( \Large \sqrt{15} =3.88\),then what is the value of \( \Large \sqrt{\frac{5}{3}} \).

A). 1.29333....

B). 1.2934

C). 1.29

D). 1.295

8). The ratinalising factor of \( \Large 3\sqrt{3} \) is:

A). \( \Large \frac{1}{3}\)

B). 3

C). -3

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

9). \( \Large \sqrt{2+\sqrt{2+\sqrt{2+...}}} \) is equal to:

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

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

C). 2

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10). The value of\( \Large 2+\sqrt{0.09}-\sqrt[3]{0.008}-7%\) of 2.80 is:

A). 0

B). 0.01

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