Question

I need help with: SquareRoot 12 + 3 SquareRoot 75 =

and

SquareRoot 20 + 2 SquareRoot 45 - 3 SquareRoot 80 =

Or any guidance of how to do them?.
Thanks

Answer 1

\[\sqrt{12} + 3\sqrt{75}\] and \[\sqrt{20} + 2\sqrt{45} - 3\sqrt{80}\]

Answer 2

\[12=4\times 3\] so
\[\sqrt{12}=\sqrt{4\times 3}=\sqrt{4}\times \sqrt{3}=2\sqrt{3}\]

Answer 3

similarly
\[75=25\times 3\] and so
\[\sqrt{75}=5\sqrt{3}\]

Answer 4

s o your first question is
\[sqrt{12}+3\sqrt{75}=2\sqrt{3}+3\times 5\sqrt{3}=2\sqrt{3}+15\sqrt{3}=18\sqrt{3}\]

Answer 5

its pretty easy, just check if perfect squares are factors of the think under the sqrt

Answer 6

actually 2 + 15 = 17 doesn't it?

Answer 7

1,4,9,16,25,36 ... etc

Answer 8

like for sqrt (80)

16 x 5 = 80

Answer 9

so i suppose unless i made some other mistake
\[17\sqrt{3}\] is it

Answer 10

and 16 is 4^2

Answer 11

so sqrt(80) = 4 sqrt(5)

Answer 12

Thank You very much for the explanation satellite and also thank you elecengineer !

Answer 13

for the second question

sqrt(20)

4 is a factor of 20


so that = sqrt(2^2 x 5 ) = sqrt(2^2) x sqrt(5) = 2sqrt(5)

Answer 14

similairly with 45, 9 is a factor , which is 3^2