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How do you find a one-decimal place approximation for #root4 45#?

Answer 1

To find a one-decimal place approximation for ( \sqrt[4]{45} ), you can use trial and error or a calculator. By trying different values, you can see that ( \sqrt[4]{45} \approx 2.9 ).

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Answer 2

Eva Abramson

#root(4)45=2.6# by calculator

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Answer 3

Ethan Adkins

Use rational approximations for #sqrt(3)# and #sqrt(5)# to find

#root(4)(45) ~~ 2.6#

#root(4)(45) = sqrt(sqrt(45)) = sqrt(sqrt(3^2*5)) = sqrt(3) sqrt(sqrt(5))#

#sqrt(3) ~~ 7/4#

#sqrt(sqrt(5)) ~~ sqrt(9/4) = 3/2#

Thus

#root(4)(45) ~~ 7/4 * 3/2 = 21 / 8 = 2.625 ~~ 2.6#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.