Question

How do you simplify `sqrt3*sqrt6`?

Answer 1

`3sqrt2`

Explanation:

`"using the "color(blue)"laws of radicals"`

`color(orange)"Reminder" sqrtaxxsqrtbhArrsqrt(ab)`

`rArrsqrt3xxsqrt6=sqrt(3xx6)=sqrt18`

`sqrt18=sqrt(9xx2)=sqrt9xxsqrt2=3xxsqrt2`

`rArrsqrt3xxsqrt6=3sqrt2`

Answer 2

`=3sqrt2`

Explanation:

Remember that if you multiplying or dividing square roots, you can combine them into one.

`sqrt3 xx sqrt6 = sqrt(3xx6)" "larr` factor `6`

`= sqrt (3xx3xx2) = sqrt(3^2xx2)`

Now find the roots where possible:

`=3sqrt2`

Answer 3

`color(blue)(=3sqrt2`

Explanation:

`sqrt3*sqrt6`

`:.=sqrt(6*3)`

`:.=sqrt(2*ul(3*3))`

`:.=sqrt3 xx sqrt3=3`

`:.color(blue)(=3sqrt2`

check:

`:.color(blue)(sqrt3 xx sqrt6=4.242640687`

`:.color(blue)(3 xx sqrt2 =4.242640687`