Question

8. Find the square root of (x2 + 4x + 4).( x2 + 10x + 25) ​

Answer 1

Answer:

Step-by-step explanation:

2.Given:

x² + 10 x + 25

==> x² + 5 x + 5 x + 25 [ By splitting ]

==> x ( x + 5 ) + 5 ( x + 5 ) [ Taking common ]

==> ( x + 5 )( x + 5 )

==> ( x + 5 )²

The square root of ( x + 5 )² is x + 5

Answer 2

${x}^{2} + 4x + 4$

$= {x}^{2} + 2x + 2x + 4$

$= x(x + 2) + 2(x + 2)$

$= {(x + 2)}^{2}$

Now,

${x}^{2} + 10x + 25$

$= {x}^{2} + 5x + 5x + 25$

$= x(x + 5) + 5(x + 5)$

$= {(x + 5)}^{2}$

So,

$\sqrt{( {x}^{2} + 4x + 4)( {x}^{2} + 10x + 25)}$

$= \sqrt{ {(x + 2)}^{2} \times {(x + 5)}^{2} }$

$= (x + 2)(x + 5)$

$= {x}^{2} + 7x + 10$