How do you simplify 4 times the square root of 8 over the square root of 2?

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Answer 1 · 2018-07-23T10:12:11

#color(purple)(=> 4 * 2 = 8#

#(4 * sqrt 8) / sqrt 2#

#=> (4 * sqrt(2 * 2 * 2)) / sqrt 2#

#=> (4 * sqrt 4 * cancel(sqrt2)) / cancel sqrt2#

#=> 4 * sqrt 4#

#color(purple)(=> 4 * 2 = 8#

Answer 2 · 2018-07-23T20:20:38

8

Breaking the question down into its component parts.

4 times#" "..................................." "4xx?#

the square root of 8#" "................." "4xxsqrt(8)#

over the square root of 2#" "..........." "4xxsqrt8/sqrt2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Did you know you can write this like: #4xxsqrt(8/2)#

It has exactly the same value. Test it with a calculator.

#4xxsqrt(4)#

#4xx2=8#

Answer 3 · 2018-07-23T20:31:51

#8#

We have the following:

#(4*sqrt8)/sqrt2#

We can start by rationalizing the denominator. We can multiply this expression by #sqrt2/sqrt2# to get

#(4sqrt8sqrt2)/2#

Recall that #sqrtasqrtb=sqrt(ab)#. With this in mind, we can condense the radicals as

#(4sqrt16)/2=(4*cancel4^2)/cancel2=4*2=color(blue)8#

Our expression simplifies to #8#.

Hope this helps!