Question

Find the Square root of :

$\sqrt{(x - y)(y - z)} + \sqrt{(y - z)(x - z)} + \sqrt{(z - x)(x - y)}$
​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{ \sqrt{( {x}^{2} + {y}^{2} - {z}^{2} - 3xy + xz + yz }) }}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}}$

$\tt: \implies \sqrt{(x - y)(y - z)} + \sqrt{(y - z)(x - z)} + \sqrt{(z - x)(x - y)}$

$\red{\underline \bold{To \: Find :}}$

$\tt: \implies the \: square \: root$

• Given Question

$\tt: \implies \: squaring - both \: sides$

$\tt: \implies\bigg[(x - y) \: (y - z)\bigg] + \bigg[(y - z) \: (x - z)\bigg] + \bigg[(z - x) \: (x - y)\bigg]$

$\tt: \implies xy - zx - {y}^{2} + yz + xy - zy - xz - {z}^{2} + xz - yz - {x}^{2} + xy$

$\tt: \implies - {x}^{2} - {y}^{2} + {z}^{2} + 3xy - xz - yz$

$\tt: \implies taking - square \: root - back$

$\green{\tt{\therefore{ \sqrt{( {x}^{2} + {y}^{2} - {z}^{2} - 3xy + xz + yz }) }}}$

Answer 2

Step-by-step explanation:

The Square Root Calculator will find the square root of the number you enter. Number. Square Root. Related Topic How to calculate square roots without ...