If a < 0, reduce the absolute value of A-3 minus the value of square a under the root sign

If a < 0, reduce the absolute value of A-3 minus the value of square a under the root sign

The absolute value of A-3 minus the value of square a under the root sign
=3-a-（-a）
=3-a+a
=3
Just one value

What is the absolute value of 1 minus root 2

┃1-√2┃=√2-1

Absolute value of root 2 minus root 3

│√2-√3│=√3-√2

Given that the absolute value of A-3 and the root sign B + 1 are opposite to each other, find the square root of a + B

The absolute value is nonnegative
Nonnegative value under radical
Because A-3 + √ (B + 1) = 0
So A-3 = 0
A=3
b+1=0
b=-1
a+b=2
Then the square roots are √ 2 and - √ 2

Given that a is the arithmetic square root of 3, B is the opposite number of root 3, the absolute value of C is the root 3 minus 1, and C is less than 0, find the value of a + B + C

A = √ 3, B = - √ 3, C = √ 3-1, C < 0, so C = 1 - √ 3
A+B+C
=√3-√3+1-√3
=1-√3

Given that the absolute values of the radical X-9 and y + 5 are opposite to each other, find the square root of X + y

The absolute values of the radical X-9 and y + 5 are opposite to each other
Then √ (X-9) + | y + 5 | = 0
Then X-9 = 0, y + 5 = 0
Then x = 9, y = - 5
Then the square root of X + y = √ (9-5) = √ 4 = 2

If the absolute values of x-2y + 9 and x-y-3 are opposite to each other, then the value of X + y is

The arithmetic square root and the absolute value term are both nonnegative, and they are opposite numbers to each other. Only the opposite number of 0 is 0, both are nonnegative
x-2y+9=0 (1)
x-y-3=0 (2)
(2)-(1)
y-12=0
y=12
Substituting (2)
x=y+3=12+3=15
x=15 y=12

Given that the absolute value 3x-y-1 and the root sign of absolute value 2x + y-4 are opposite numbers to each other, find the arithmetic square root of X + 4Y

Absolute value of 3x-y-1 > = 0
Radical 2x + y-4 > = 0
The absolute value of 3x-y-1 is opposite to the radical 2x + y-4
therefore
Absolute value of 3x-y-1 = 0
Radical 2x + y-4 = 0
So x = 1, y = 2;
The arithmetic square root of X + 4Y is positive = root sign (1 + 4 * 2) = 3

The arithmetic square root of 81 is______ .

∵92=81，
Qi
81=9．
So the answer is: 9

Find the square root of 81 and the arithmetic square root of root 81

The square roots of 81 are + 9 and - 9
The arithmetic square root of the root 81 is 3 (the root 81 should have no sign before it, so it is determined to be positive 9)