Question

Please help 7√ ̅45 + 5√ ̅48 ?
thanks.

Answer 1

Simplify each radical part using the method I told you here:
http://openstudy.com/study#/updates/5224ab30e4b06211a67f88a8

Then, if you have "like radicals" - meaning that they have the SAME thing under the square root - you can combine them with addition because they are "like terms". If you DONT have like terms, then you can't, and the expression is fully simplified.

Answer 2

Eg.:

\[\Large 5\sqrt{12}+2\sqrt{29}=5\sqrt{4\cdot3}+2\sqrt{9\cdot3}\\\Large=5\cdot2\sqrt{3}+2\cdot3\sqrt{3}\\\Large=10\sqrt{3}+6\sqrt{3}~~~\leftarrow\text{these are like terms so they combine}\\\Large=16\sqrt{3}\]

\[\Large 5\sqrt{12}+2\sqrt{20}=5\sqrt{4\cdot3}+2\sqrt{4\cdot5}\\\Large=5\cdot2\sqrt{3}+2\cdot2\sqrt{5}\\\Large=10\sqrt{3}+4\sqrt{5}~~~\leftarrow\text{these are NOT like terms, CAN'T combine}\\\]