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How to find a cube root geometrically?

How do you find the cube root of the square root of eight?

  • Answer:

    You know that (x^a)^b == x^(ab) So [8^(1/2)]^(1/3) == 8^(1/6) So that is your answer, the cube root of the square root of eight is 8^(1/6), or "the sixth root of eight" If you want to simplify it, you know that 8 == 2^3, so 8^(1/6) == 2^(3/6) or simply 2^(1/2) which is "the square root of 2"

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First you find the square root of 8 (which number multiplied by itself results in 8?): 2.8284271247461903 Second you find the cube root of 2.8284271247461903: 1.4142135623730951 Your answer is 1.414213562373095 (I might add it is approximate due to infinite decimals). Any questions?

AntigoneRising

sq. root 8 first and then cb. root what is left.

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