Question

I need help with simplifying

Answer 1

\[6a \sqrt{80b}-\sqrt{180a ^{2}b}+5a \sqrt{b}\]

Answer 2

Look at the middle term and take the prime factorization of 180

Answer 3

Do the same for 80

Answer 4

60 & 2 for 180 then 40&2 for 80
right?

Answer 5

\[6a\sqrt{20\cdot 2 \cdot 2 \cdot b}- \sqrt{20 \cdot 9 \cdot a\cdot a \cdot b}+5a\sqrt{b}\]

Answer 6

\[60 \cdot 2 \ne 180\]

Answer 7

lol i had meant 90

Answer 8

Yes that works too :)

Answer 9

now factor both 20's and the 9 into simpler, prime factors.

Answer 10

10 x 2 for 20's & 3 x 3 for 9

Answer 11

Good. \[6a\sqrt{10\cdot 2\cdot 2 \cdot 2 \cdot b}- \sqrt{10 \cdot 2 \cdot 3\cdot 3 \cdot a\cdot a \cdot b}+5a\sqrt{b}\]

Answer 12

factor both 10's one more time into prime factors.

Answer 13

5 & 2

Answer 14

Great \(\checkmark\) \[6a\sqrt{5\cdot 2\cdot 2\cdot 2 \cdot 2 \cdot b}- \sqrt{5\cdot 2 \cdot 2 \cdot 3\cdot 3 \cdot a\cdot a \cdot b}+5a\sqrt{b}\]

Answer 15

Now for every fair of 2 numbers, 1 of them will be extracted from the square root and multiplied to the term outside the square root.

Answer 16

pair*

Answer 17

For example, to start you off. \[6a\sqrt{5\color{blue}{\cdot 2\cdot 2}\color{red}{\cdot 2 \cdot 2} \cdot b} = 6a \cdot \color{blue}{2} \cdot \color{red}{2}\sqrt{5 \cdot b}\]

Answer 18

\[48a \sqrt{5\times2timesb}-6a \sqrt{5\times2\times3 \times a \times b}+5a \sqrt{b}\]

Answer 19

Not quite. In the first part you still have a 2 left within the square root when its been paired off and pulled out already. You should just have a 5 and a b left within the square root there since they are lone pairs and cannot be pulled out. Once things are paired off, they are not rewritten within the square root.

Second part, the 6a looks right, therefore the only thing that should be left within the square root should be 5 and b.

Answer 20

ohh okay i think i got it now

Answer 21

It should look like this: \[6a\sqrt{5\color{blue}{\cdot 2\cdot 2}\color{red}{\cdot 2 \cdot 2} \cdot b} = 6a \cdot \color{blue}{2} \cdot \color{red}{2}\sqrt{5 \cdot b} = 24a\sqrt{5b}\]\[- \sqrt{5\cdot\color{red}{ 2 \cdot 2} \cdot \color{blue}{3\cdot 3} \cdot \color{green}{a\cdot a} \cdot b} = -6a\sqrt{5b}\]

Answer 22

yeah thats what i got