# What is the square root of the square root of the square root of 100, in radical form?What is the square root of the square root of the square root of 100, in radical form?

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It is the fourth root of 10 -- square root of square root of square root of 100 is the square root of the square root of 10. Assign this value to x and square both sides -- then x^2=sqrt(10); squaring again yields x^4=10 or x=the fourth root of 10.

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square root of 100=10

square root of 10=10 raised to the power of 0.5=10^1/2

square root of square root of 10=(10^1/2)^1/2

this is the same as 10^(1/2)x(1/2)

1/2 multiplied by 1/2=1/4

hence square root of square root of square root of 100=10^1/4

the pleasure was all mine.

Posted on

The radical would have a fourth index

I prefer to use exponents.

100^0.25

=1.414

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square root of 100 is 10

there are 2 more square roots ,so we can write it as (10^1/2)^1/2

that is 10 1/2*1/2=10^1/4

=4th root of 10

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