Question

Which is the exact value of the expression the square root of 48. − the square root of 75. + the square root of 192.?

Answer 1

gimmick here is to find the largest perfect square that is a factor of 48

Answer 2

any ideas for that one ?

Answer 3

36?

Answer 4

here is my example for \(75\)
the largest perfect square that is a factor of \(75\) is \(25\) because \(75=25\times 3\)

Answer 5

and therefore \(\sqrt{75}=\sqrt{25\times 3}=\sqrt{25}\sqrt{3}=5\sqrt{3}\)

Answer 6

no not 36
i did not mean the greatest perfect square less than 48, but rather the greatest perfect square that is a FACTOR of 48

Answer 7

oh so 12
so it would be \[4\sqrt{3}\]

Answer 8

not 12 sorry 16

Answer 9

well yes to \(4\sqrt{3}\)

Answer 10

figured that is what you meant

Answer 11

so now we get the idea right?
\[\sqrt{48}=4\sqrt{3}\]
\[\sqrt{75}=5\sqrt{3}\]

Answer 12

i am going to bet that \(192\) is some perfect square times \(3\)

Answer 13

yes so for 192 it would be \[8\sqrt{3}\]

Answer 14

if \(192=3\times 64\) then yes

Answer 15

so last job is to combine like terms

Answer 16

Then the new equation is \[4\sqrt{3}-5\sqrt{3}+8\sqrt{3}\]
then combine like terms

Answer 17

so the answer is \[7\sqrt{3}\]

Answer 18

yes

Answer 19

Thank you so much

Answer 20

yw