when √(a²+x²)
The expression √(a²+x²) represents the square root of the sum of the squares of the numbers a and x
The expression √(a²+x²) represents the square root of the sum of the squares of the numbers a and x. In mathematics, this expression is commonly encountered in geometry and calculus, particularly when dealing with right triangles and distance calculations.
To simplify this expression, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem to the expression √(a²+x²), we can rewrite it as √a² + √x². Since both a² and x² are non-negative (since they are squared), the square root can be written as a separate term for each.
Therefore, √(a²+x²) simplifies to √a² + √x², which can be further simplified to a + x. So, √(a²+x²) is equal to a + x.
It is important to note that this simplification is valid only when a and x are positive numbers. If a or x is negative, then we have to consider the absolute value of a and x in order to compute the result accurately.
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