Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

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

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

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

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

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

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

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!