Question:
Find the value
$x^{2}+5 \sqrt{5} x+30$
Solution:
Splitting the middle term,
$=x^{2}+2 \sqrt{5} x+3 \sqrt{5} x+30$
$[\therefore 5 \sqrt{5}=2 \sqrt{5}+3 \sqrt{5}$ also $2 \sqrt{5} \times 3 \sqrt{5}=30]$
$=x(x+2 \sqrt{5})+3 \sqrt{5}(x+2 \sqrt{5})$
$=(x+2 \sqrt{5})(x+3 \sqrt{5})$
$\therefore x^{2}+5 \sqrt{5} x+30$
$=(x+2 \sqrt{5})(x+3 \sqrt{5})$