How do you simplify \sqrt { 50x ^ { 6} y ^ { 8} } 50x6y8?

2 Answers
Jun 16, 2017

See a solution process below:

Explanation:

We can rewrite this expression as:

sqrt(25x^6y^8 * 2)25x6y82

Now, using this rule for radicals we can simplify the expression:

sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))ab=ab

sqrt(color(red)(25x^6y^8) * color(blue)(2)) =>25x6y82

sqrt(color(red)(25x^6y^8)) * sqrt(color(blue)(2)) =>25x6y82

5x^3y^4 * sqrt(color(blue)(2)) =>5x3y42

5x^3y^4sqrt(2)5x3y42

Jun 16, 2017

5x^3y^4sqrt25x3y42

Explanation:

I start by separating the coefficient (number) and variables.

What is the square root for 50?

50 breaks up into 25 xx 225×2. You want to use 25 because it's a perfect square and easy to find the square root.

sqrt 50 = sqrt 25 sqrt 250=252

The square root of 25 is 5 so can be simplified further:
sqrt 50 = sqrt 25 sqrt 2= 5 sqrt 250=252=52

Now look at the variables. You should divided the exponents by 2. That number will go on the outside of the root. If there is any remainder that will go on the inside of the room.

sqrt (x^6 y^8) x6y8

look at x^6x6 take the 6 divide it by 2...you get 3.
so it looks like

x^3 sqrt (y^8)x3y8

now you have the y^8y8 take the 8 divide it by 2..you get 4 so it looks like

x^3 y^4x3y4

Now combine squish your parts together. Parts outside of the square root stay together and parts inside the square root go together.

5x^3y^4sqrt25x3y42

DONE!!