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

3 Answers
Jul 23, 2018

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

Explanation:

(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

Jul 23, 2018

8

Explanation:

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

Jul 23, 2018

8

Explanation:

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!