Try without a calculator!

Algebra Level 3

Find the value of: − 2 − 2 − 2 { -2 }^{ { -2 }^{ -2 } }


The answer is -0.84089641525371.

Mohamed Aly by Mohamed Aly , 49, Egypt

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1 solution

− 2 − 2 − 2 = − 2 − 1 2 2 = − 1 2 4 = − 2 3 / 4 2 ≈ − 0.8408 \large{-2^{{-2}^{-2}} = -2^{-\frac{1}{2^2}}=-\frac{1}{\sqrt[4]{2}}} =-\frac{2^{3/4}}{2} \approx \boxed{-0.8408}

I still cannot know to evaluate the last step without a calculator.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That's right ! You can't calculate further unless you are a calculator :P

Rohit Udaiwal - 5 years, 8 months ago

in the second step -2^(-2)=(-1/2)^2=1/4 so why -1/4

Harshi Singh - 5 years, 8 months ago

I'm guessing the title is just sarcasm

James Wilson - 3 years, 6 months ago

just find the square root of the square root of 8 (by the manual method) and divide by 2

Bob Kadylo - 3 years, 3 months ago

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