Question

What is the product of 2the square root of the quantity 10 times k. • 5kthe square root of 2.? Simplify if possible.

@Nurali

Answer 1

@zepdrix

Answer 2

Like this? :o\[\Large 2\sqrt{10k}\cdot5k\sqrt{2}\]

Answer 3

yes :o

Answer 4

So we have a big bundle of multiplication here.
Since multiplication is `commutative`, we can multiply in any order.
Let's start by moving the 5k to the front and then multiply the 5 and 2 together.\[\Large 2\cdot5k\sqrt{10k}\cdot\sqrt{2} \qquad=\qquad 10k\sqrt{10k}\cdot\sqrt2\]

Answer 5

@zepdrix ? o.o

Answer 6

We can break down the first square root term like this,
\[\Large 10k\sqrt{k}\sqrt{10}\cdot\sqrt2\]
Let's break down the 10 a little bit,\[\Large 10k\sqrt{k}\sqrt{5\cdot2}\cdot\sqrt2 =10k\sqrt{k}\sqrt{5}\color{royalblue}{\sqrt{2}\cdot\sqrt2}\]

Confused by any of those steps?
Do you understand what this blue portion gives us when we multiply it out?

Answer 7

I don't understand the second part.

Answer 8

I rewrote 10 as 5times2.
Is that the part that was confusing? :o

Answer 9

Oh oh maybe this would be easier...

Answer 10

\[\Large 10k\sqrt{10k}\cdot\sqrt2 =10k\sqrt{10k\cdot2}\]Combining the roots by bringing the 2 in.
Now we can multiply the 2 and 10,\[\Large 10k\sqrt{20k}\]Does this way make a little bit more sense maybe? :O

Answer 11

From here, there is a factor of 20 that is a perfect square.
So we'll factor our 20 into 4x5.\[\Large 10k\sqrt{4\cdot5k}\]Taking the square root of 4 gives us? :o

Answer 12

2 x 5k :o ?

Answer 13

\[\Large 10k\cdot2\sqrt{5k}\]
Good good.
So as a final step it looks like you can multiply the 10 and 2 :O

Answer 14

20k! :) Thanks.

Answer 15

Yay good job \c:/
\[\Large 20k\sqrt{5k}\]