What is the square root of 5 divided by the square root of 8?

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Answer 1 · 2018-06-15T02:58:03

#sqrt10/4# or #~~0.79#

We have the following

#sqrt5/sqrt8#

The convention is to not have an irrational number in the denominator, so to get rid of it, we can multiply the top and bottom by #sqrt8#. We get

#(sqrt5*sqrt8)/(sqrt8)^2#

Which simplifies to

#sqrt40/8#

We can rewrite this as

#sqrt(4*10)/8#

#=>(2sqrt10)/8#

#=>color(blue)(sqrt10/4)#

As a decimal, this is approximately

#0.79#

Hope this helps!

Answer 2 · 2018-06-15T02:59:01

#sqrt10/4#

Let's translate this into mathematical terms:

square root of 5: #sqrt5#

square root of 8: #sqrt8#

Since we divide them, it becomes:
#sqrt5/sqrt8#

If you want to simplify this, we can multiply both numerator and denominator by #sqrt8#:
#sqrt5/sqrt8 * sqrt8/sqrt8#

Simplify:
#sqrt40/8#

#sqrt(4*10)/8#

#(sqrt4sqrt10)/8#

#(2sqrt10)/8#

#sqrt10/4#

Hope this helps!