Factorize:$x^2 + 5\sqrt{5}x + 30$

Given :

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

To do :

We have to factorize the given expression.

Solution :

$x^2 +5 \sqrt{5}x + 30=x^{2}+3 \sqrt{5} x+ 2\sqrt{5} x+30$                  [Since $3\sqrt{5} x+2\sqrt{5} x=5\sqrt{5} x$ and $3 \sqrt{5} x\times2\sqrt{5} x=30\times x^2$]

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

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

Hence, $x^2 +5 \sqrt{5}x + 30=(x+2 \sqrt{5})(x+3\sqrt{5})$.

Tutorialspoint

Updated on: 10-Oct-2022

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