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Geometric Estimation Value of Square Root

√2√7-3√3×√55+...

Question

$\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} \times \sqrt[4020]{55 + 12 \sqrt{21}}$ is equal to

A

- 1

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B

1

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C

0

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D

2

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Solution

The correct option is D $1$
$\Rightarrow$ $\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} \times \sqrt[4020]{55 + 12 \sqrt{21}}$

$\Rightarrow$ $\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} \times {\sqrt[4020]{(2 \sqrt{7} + 3 \sqrt{3})}}^{2}$

$\Rightarrow$ $\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} \times \sqrt[2010]{2 \sqrt{7} + 3 \sqrt{3}}$

$\Rightarrow$ $\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3} (2 \sqrt{7} + 3 \sqrt{3})} = \sqrt[2010]{(28 - 27)} = 1$

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Similar questions

\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} \times \sqrt[4020]{55 + 12 \sqrt{21}} = ?

Q. The value of

\sqrt{(\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}}) (\sqrt[4020]{55 + 12 \sqrt{21}})}

Q. The value of

\sqrt[2010]{(2 \sqrt{7} - 3 \sqrt{3}) \sqrt{55 + 12 \sqrt{21}}}

Solve:

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i)

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(\sqrt{3} + 1)^{2} - (\sqrt{3} - 1)^{2}

(2 + \sqrt{5})^{5} + (2 - \sqrt{5})^{5}

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