Find the value

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 $2 \sqrt{5} \times 3 \sqrt{5}=30]$

$=x(x+2 \sqrt{5})+3 \sqrt{5}(x+2 \sqrt{5})$

$=(x+2 \sqrt{5})(x+3 \sqrt{5})$

$\therefore x^{2}+5 \sqrt{5} x+30$

$=(x+2 \sqrt{5})(x+3 \sqrt{5})$

 

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