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

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Answer 1 · 2015-10-16T19:16:33

$root(4)45=2.6$ by calculator

$root(4)45=2.6$ by calculator

Answer 2 · 2015-10-16T20:40:12

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

$root(4)(45) ~~ 2.6$

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

$sqrt(3) ~~ 7/4$

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

So

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

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