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The 100th root of $10^{{(10)}^{10}}$ is:

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10^{{(8)}^{10}}

10^{{(10)}^{8}}

{\sqrt{10}}^{{(\sqrt{10})}^{8}}

10 ({\sqrt{10}}^{\sqrt{10}})

answer is B.

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Detailed Solution

Concept- Let the required value is

x

. If we multiply

x

for

100 times

we will get

10^{{(10)}^{10}}

. All we need to do is form an equation that can suffice with the question and yield us an answer.
Let the number is

x

.
Therefore the

100 th

root of

10^{{(10)}^{10}}

x

.
That means if we multiply

x

for

100 times

we will get

10^{{(10)}^{10}}

.
Or we can say if we take

x

to the power 100 we will get

10^{{(10)}^{10}}

.
Hence,

x^{100} = 10^{{(10)}^{10}}

From this equation we have to find out the value of xx.
Therefore we have,

x^{100} = 10^{{(10)}^{10}}

\Rightarrow x = {(10^{{(10)}^{10}})}^{\frac{1}{100}}

\Rightarrow x = 10^{\frac{10^{10}}{10 \times 10}}

\Rightarrow x = 10^{\frac{10^{10}}{10 \times 10}}

\Rightarrow x = 10^{\frac{10^{10}}{10^{2}}}

\Rightarrow x = 10^{10 - 2}

\Rightarrow x = 10^{8}

Therefore, the 100th root of

10^{{(10)}^{10}}

10^{{(10)}^{8}}

.
Hence, option (2) is correct.

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