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What is the square root of the square root of the square root of 100, in radical...

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elekzy | Student, Grade 11 | Valedictorian

Posted March 25, 2012 at 11:51 AM via web

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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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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted March 25, 2012 at 1:06 PM (Answer #2)

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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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takmingw | eNotes Newbie

Posted March 26, 2012 at 1:46 PM (Answer #3)

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The answer is 1.77827941 so about 1.8

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khansaqib | Student , Grade 9 | Honors

Posted April 8, 2012 at 6:49 AM (Answer #5)

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  • The ans is square root 3.16227766 .
  •  In simple form =1.77
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prabudh | Student , Grade 9 | Honors

Posted April 10, 2012 at 3:26 PM (Answer #7)

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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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yaozhang | eNoter

Posted April 17, 2012 at 6:23 AM (Answer #8)

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The answer is approx 1.77

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utilityfan | Student , College Freshman | Valedictorian

Posted April 20, 2012 at 8:08 PM (Answer #9)

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The radical would have a fourth index

I prefer to use exponents.

100^0.25

=1.414

 

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harshdeawesome | Student , Grade 9 | eNoter

Posted May 6, 2012 at 8:02 AM (Answer #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.

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