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

##### 2 Answers

Oct 16, 2015

#### Explanation:

Oct 16, 2015

Use rational approximations for

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

#### Explanation:

#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#