Question

square root of x

power 6 + 8 x power 4 minus 2 x power 3 + 16 x power 2 - 8x + 1 using division method ​

Answer 1

SOLUTION

TO DETERMINE

The square root of

$\sf{ {x}^{6} + 8 {x}^{4} - 2 {x}^{3} + 16 {x}^{2} - 8x + 1 }$

EVALUATION

Here the given expression is

$\sf{ {x}^{6} + 8 {x}^{4} - 2 {x}^{3} + 16 {x}^{2} - 8x + 1 }$

Division : Division is referred to the attachment

Procedure :

Step : 1

The quotient is

$\sf{ {x}^{6} + 8 {x}^{4} - 2 {x}^{3} + 16 {x}^{2} - 8x + 1 }$

The Divisor is x³

Step : 2

We take three terms

$\sf{ 8 {x}^{4} - 2 {x}^{3} + 16 {x}^{2} }$

The Divisor is 2x³ + 4x

Step : 3

We take the remaining two Terms so that the quotient is

$\sf{ - 2 {x}^{3} - 8x + 1 }$

The Divisor is 2x³ + 8x - 1

FINAL ANSWER

Hence the required square root

$\sf{ = {x}^{3} + 4x - 1 }$

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