What is the difference between square root and arithmetic square root Every time I do a question, I hesitate. I don't know what the square root of 16 is, whether it's plus or minus 4 or 4,

What is the difference between square root and arithmetic square root Every time I do a question, I hesitate. I don't know what the square root of 16 is, whether it's plus or minus 4 or 4,

What's the square root of 16? It's plus or minus 4
What's the arithmetic square root of 16? It's positive 4
Square root and arithmetic square root
There are two more square roots of positive numbers
There is only one arithmetic square root, which is the positive one

Two square root questions
If √ X-2 and √ Y-X + 1 are opposite to each other, find X and y
If the square root of Y is x + 1 and 2x-1, find y

√ X-2 and √ Y-X + 1 are opposite to each other √ X-2 + √ Y-X + 1 = 0
∵ √ X-2 and √ Y-X + 1 are both non negative numbers √ X-2 = 0 √ Y-X + 1 = 0  x = 2, y = 1
The square root of Y is x + 1 and 2x-1 ｛ x + 1 + 2x-1 = 0 ｛ x = 0 x + 1 = 1 2x-1 = - 1
∴y=1

Square root solution
Given x = radical 2 + radical 5. Y = radical 5 - radical 2, find the square of X - XY + y square

Square of X - XY + y square = square of X - 2XY + y square + XY
=(x+y)^2+xy
=(radical 2 + radical 5 + radical 5-radical 2) ^ 2
+(radical 2 + radical 5) × (radical 5-radical 2)
=(2 × radical 5) ^ 2 + (radical 5) ^ 2 - (radical 2) ^ 2
=23