Question:
Find the value
$x^{2}+6 \sqrt{2} x+10$
Solution:
Splitting the middle term,
$=x^{2}+5 \sqrt{2} x+\sqrt{2} x+10$
$[\therefore 6 \sqrt{2}=5 \sqrt{2}+\sqrt{2}$ and $5 \sqrt{2} \times \sqrt{2}=10]$
$=x(x+5 \sqrt{2})+\sqrt{2}(x+5 \sqrt{2})$
$=(x+5 \sqrt{2})(x+\sqrt{2})$
$\therefore x^{2}+6 \sqrt{2} x+10$
$=(x+5 \sqrt{2})(x+\sqrt{2})$