Question

Find the square root of the following expressions
256(x - a)2 (x - b)4 (x - c)16 (x - d)20

Answer 1

Given  : Expression :

256 (x-a)2 (x-b)4 (x-c)16 (x-d)20

To Find : Square root

Solution:

256(x-a)²(x-b)⁴(x-c)¹⁶(x-d)²⁰

256 = 16²

(x-b)⁴ = (x-b)²ˣ²

using   (x)ᵃˣᵇ =  (xᵃ)ᵇ

Hence  (x-b)²ˣ²  =  ((x -b)²)²

=> (x-b)⁸ =  ((x -b)²)²

Similarly

(x-c)¹⁶ =  ((x -c)⁸)²

(x-d)²⁰  =  ((x -d)¹⁰)²

256(x-a)⁸(x-b)⁴(x-c)¹⁶(x-d)²⁰

= 16² ((x -a))²((x -a)⁴)² ((x -b)²)² ((x -c)⁸)²  ((x -d)¹⁰)²

Using aⁿ * bⁿ = (a b)ⁿ

= ( 16 (x -a)(x -b)²(x -c)⁸(x -d)¹⁰)²

√a² = a

Hence square root of   ( 16 (x -a)(x -b)²(x -c)⁸(x -d)¹⁰)²

=  16 (x -a)(x -b)²(x -c)⁸(x -d)¹⁰

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