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# The statement “the sum of the squares of $x$ and $y$ is equal to the square root of the difference of $x$ and $y$” can be mathematically represented as:A.${x^2} + {y^2} = \sqrt {x - y}$B.${x^2} - {y^2} = \sqrt {x + y}$C.${\left( {x + y} \right)^2} = \sqrt x - \sqrt y$D.$\sqrt {x + y} = {\left( {x - y} \right)^2}$

Last updated date: 20th Jun 2024
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Answer
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Hint: Here, we will take the squares of $x$ and $y$ and then add them. Then we will take the obtained sum as equal to the square root of the difference of $x$ and $y$.

Complete step-by-step answer:
First, we will find the square of $x$.
$\Rightarrow {x^2}{\text{ .......eq.(1)}}$
Then we will find the square of $y$.
$\Rightarrow {y^2}{\text{ .......eq.(2)}}$
Adding the equation (1) and equation (2), we get
$\Rightarrow {x^2} + {y^2}{\text{ ......eq.(3)}}$
Subtracting $y$ from $x$, we get
$\Rightarrow x - y$
Taking the square root in the above equation, we get
$\Rightarrow \sqrt {x - y} {\text{ .....eq.(4)}}$
Taking equation (3) equal to equation (4) as given in the problem, we get
$\Rightarrow {x^2} + {y^2} = \sqrt {x - y}$
Hence, option A is correct.

Note: We need to know that the mathematical representation of a statement is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. This problem is simple, we just have to follow each step by step properly. Avoid calculation mistakes.