multiply and simplify by factoring?

√10 = √5 * √2

√15 = √5 * √3

5√5*√2 * 3√5*√3 = 5 * 3 * √5 * √5 * √2 * √3 = 5 * 3 * 5 * √2 * √3 = 75√6

Multiply And Simplify By Factoring

5√10 · 3√15

= 15√150

= 15√(25 · 6)

= 15 · 5 · √6

= 75√6

Hello Sofia, product of rational numbers 5and 3 gives 15

And product of irrationals gives ./150 = ./25*6 = 5./6

So the final product would be 15*5*./6 = 75./6

5√10 · 3√15

=5 ·√2 ·√5 ·3 ·√5 ·

= 15·5·

=75√6

It doesn't simplify much.

5*sqrt(2)*sqrt(5) - 3*sqrt(3)*sqrt(5)

sqrt(5) [ 5sqrt(2) - 3 sqrt(3)] which is all you can do.

You might want to convince yourself that sqrt(10) = sqrt(2)*sqrt(5)

Sqrt(10) = 3.162278

Sqrt(2)*sqrt(5) = 1.4142*2.236 =3.1622.

The disagreement to further decimal places happens because I rounded.

Edit

===

I took that dot in the middle to be a minus which it's not. My answer is wrong, but some of the explanation will help you.

The correct answer is 5*sqrt(2)*sqrt(5)*3*sqrt(3)*sqrt(5) = 75 sqrt(6)

sqrt(5)*sqrt(5) = 5

sqrt(3)*sqrt(2) = sqrt(6)

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RE:

multiply and simplify by factoring?

please I really need help solving these problem. If you can please explain it to me, thank you!!

multiply and simplify by factoring:

5√10 · 3√15

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i dont understand the question.. sorry but if i did i really could help