Question

find the square root of 256 (x-a)8 (x-b)4 (x-c)16 (x-d)20

Answer 1

Given,

$\[256{\left( {x - a} \right)^8}{\left( {x - b} \right)^4}{\left( {x - c} \right)^{16}}{\left( {x - d} \right)^{20}}\]$

Solution,

Calculate the square root.

$\[\begin{array}{l} = \sqrt {256{{\left( {x - a} \right)}^8}{{\left( {x - b} \right)}^4}{{\left( {x - c} \right)}^{16}}{{\left( {x - d} \right)}^{20}}} \\ = \sqrt {{{16}^2}{{\left( {x - a} \right)}^8}{{\left( {x - b} \right)}^4}{{\left( {x - c} \right)}^{16}}{{\left( {x - d} \right)}^{20}}} \\ = 16{\left( {x - a} \right)^4}{\left( {x - b} \right)^2}{\left( {x - c} \right)^8}{\left( {x - d} \right)^{10}}\end{array}\]$

Hence the square root is $\[16{\left( {x - a} \right)^4}{\left( {x - b} \right)^2}{\left( {x - c} \right)^8}{\left( {x - d} \right)^{10}}\]$