Question

How to simplify the radical of 5√108

Answer 1

108=36 x 3

Answer 2

\[5\sqrt{108} = 5\sqrt{36*3}=5\sqrt{36}\sqrt{3}\]

36 is the square of 6

Answer 3

So what is the answer? and if 6 times 6 iquals 36 and then both 6 spreands to 3 3 3 3 ... doesnt the 5 have to multiply one of the 3's?

Answer 4

\[5\sqrt{108} = 5\sqrt{36*3}=5\sqrt{36}\sqrt{3} = 5*6*\sqrt{3} = 30\sqrt{3}\]

Answer 5

6 x 6 is not 3 x 3 x 3 x 3, 3 x 3=9

Answer 6

Yes.. I agree my mistake there.. but it could be 3x 2 plus 3x2 intead? and would the 5 multiply the 3 or 2 and why?

Answer 7

yes, you could write 36=6x6=3*2+3*2
but no need, the square root of 36 is 6

Answer 8

if you really wanted you could write this
\[5*\sqrt{36*3}=5*\sqrt{(3*2)^2 * 3} = 5*\sqrt{(3*2)^2}*\sqrt{3} = 5*(3*2)*\sqrt{3} = 30\sqrt{3}\]

Answer 9

Oh Thank you so much you helped me a lot :)!

Answer 10

welcome