How do you multiply #\sqrt { 15k } \cdot \sqrt { 10k ^ { 3} }#?

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Answer 1 · 2017-05-16T21:10:13

See a solution process below:

We can first use rule for multiplying radicals:

#sqrt(a) * sqrt(b) = sqrt(a * b)#

#sqrt(15k) * sqrt(10k^3) = sqrt(15k * 10k^3) =>#

#sqrt((15 * 10) * (k * k^3)) => sqrt(150 * k^4) => sqrt(150k^4)#

We can now rewrite this equation and use the same rule in reverse to simplify the result:

#sqrt(25 * 6 * k^4) =>sqrt(25) * sqrt(6) * sqrt(k^4) =>#

#5sqrt(6)k^2#

Or

#12.2k^2# rounded to the nearest 10th.

Answer 2 · 2017-05-16T21:13:48

#5k^2sqrt(6)#

First, combine the square roots into a single one.
#sqrt(15k*10k^3)#

Next, combine terms.
#sqrt(150*k^4)#

Next, break the terms into squares.
#sqrt(5^2*6*k^2*k^2)#

Next, pull out all the terms with squares on them. Squares and square roots cancel when the terms are multiplied or divided.
#5*k*ksqrt(6)#

Finally, simplify.
#5k^2sqrt(6)#