How do you multiply $sqrt(2x^5y^2)/sqrt(14x^3y^8)$ ?

Question

1520 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-11T00:53:03

$(xsqrt7)/(7y^3)$

First, remember that:
$sqrt (a^2b)=asqrtb$

Using our rule, we simplify the radicals.
$(sqrt (2x^5y^2))/(sqrt (14x^3y^8))$ becomes $(yx^2sqrt (2x))/(xy^4sqrt (14x))$

We now try to rationalize the denominator.

$(yx^2sqrt (2x))/(xy^4sqrt (14x))xx(sqrt (14x))/(sqrt (14x))=> (yx^2sqrt (2x)*sqrt(14x))/(xy^4(14x))$

Now, remember that:
$sqrt a *sqrtb=sqrt(ab)$

$(yx^2sqrt (2x)*sqrt(14x))/(xy^4(14x))$ becomes
$(yx^2sqrt (28x^2))/(xy^4(14x))$ Using our first rule, we can simplify this further.

$(yx^2sqrt (28x^2))/(xy^4(14x))=>(yx^2(2xsqrt7))/(xy^4(14x))$

We multiply this out to get:
$(2x^3ysqrt7)/(14x^2y^4)$

Lastly, remember that:
$(a^n)/(a^m)=a^(n-m)$

Using this rule, we now have:
$(xsqrt7)/(7y^3)$
This is the answer!

How do you multiply sqrt(2x^5y^2)/sqrt(14x^3y^8)sqrt(2x^5y^2)/sqrt(14x^3y^8)?