Question

Evaluate:square root of x^a-b×square root of x^b-c×square root of x^c-a

Answer 1

$\sqrt{ {x}^{(a - b)} } \times \sqrt{ {x}^{(b - c)} } \times \sqrt{ {x}^{(c - a)} } \\ \\ = \sqrt{{x}^{(a - b)} \times {x}^{(b - c)} \times {x}^{(c - a)} }$

$= \sqrt{ {x}^{[(a-b)+(b-c)+(c-a)]} } \\ \\ = \sqrt{ {x}^{[a-b+b-c+c-a]} } \\ \\ = \sqrt{ {x}^{[a-a-b+b-c+c]} } \\ \\ = \sqrt{ {x}^{0} } \\ \\ = \sqrt{1} \\ \\ = 1$

$\boxed{\bold{\red{answer : \sqrt{ {x}^{(a - b)} } \times \sqrt{ {x}^{(b - c)} } \times \sqrt{ {x}^{(c - a)} } = 1}}}$

Answer 2

$\sqrt{ {x}^{a - b} } \times \sqrt{ {x}^{b - c} } \times \sqrt{ {x}^{c - a} } \\\\ = \sqrt{ {x}^{a - b + b - c + c - a} } \\\\ = \sqrt{ {x}^{0} }\\ \\ = \sqrt{1}\\ \\ = 1$