Common Misconception: Square Root and Principal Square Root

I was bemused when our consultant showed me a certain part in our textbook and he looked so disappointed. I asked him "Why? I don't see any errors there. What's wrong, sir?"

"This is a common mistake among students, and teachers as well," he said.

We are all familiar with the radical sign (√). A radical sign with out an index (a number on the upper left part of the symbol), indicates square root.

If we say "Find the square root of 9," in symbol that is . We know that the answer to the square root of 9 is + 3 and –3. But take note that when we deal with symbols, the radical sign pertains to the principal square root of the number. The principal square root of the number is that one square root of the number that is NOT negative. Therefore, there "square root of 9" is different from .