Question

Simplify the radical expression sqrt 150x^3k^4
a)75x^3k^2
b)5xk times sqrt 6xk
c)5xk^2 times sqrt 6x
d)5 times sqrt 6x^3k^4
Please help! I tried asking people I know how to solve these types of problem but they tell me to look in the textbook. The textbook explains these problems so confusing! I'll be so so so grateful if someone out there can help me with this problem and a few others.

Answer 1

\[\huge\rm \sqrt{150x^3k^4}\]
is it your question ?

Answer 2

factor 150

Answer 3

x^3 can be written as \[\huge\rm \sqrt{x^3} =\sqrt{x \times x \times x } = \sqrt{x^2 \times x}\]
same with k^4

Answer 4

yeah \[\sqrt{150}x^3k^4\] is my question. The number's factors are 30 and 5, but I'm not sure how to factor squares. okay.

Answer 5

alright there are more factors of 150
one of number should be perfect square

Answer 6

*square roots

Answer 7

yeah square roots**

Answer 8

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
alright there are more factors of 150
one of number should be perfect square
\(\color{blue}{\text{End of Quote}}\)
perfect square roots

Answer 9

25 is a perfect square factor of 150 so should I use that?

Answer 10

yes
25 times 6 =150
so \[\sqrt{25 \times 6} = 5 \sqrt{6}\]
square root of 25 is 5

Answer 11

x^3 can be written as \[\huge\rm \sqrt{x^3} =\sqrt{x \times x \times x } = \sqrt{x^2 \times x}\]
same with k^4
did you get this one ?

Answer 12

remember when you multiply same bases you should add their exponent
so x^3 can be written as x^2 times x
i wrote x to the 2nd power so you can cancel square root with square

Answer 13

Yeah I remember that. So I factor the x and k too? I see what you are saying but how do I write that with the factored number?

Answer 14

yes right
k^4 can be written as k^2 times k^2 then you can cancle square root with squares

Answer 15

like this