Factorize:$x^2 + 6\sqrt{2}x + 10$

Given :

$x^2 + 6\sqrt{2}x + 10$

To do :

We have to factorize the given expression.

Solution :

$x^{2}+6 \sqrt{2} x+10=x^{2}+5 \sqrt{2} x+\sqrt{2} x+10$                  [Since $5 \sqrt{2} x+\sqrt{2} x=6 \sqrt{2} x$ and $5 \sqrt{2} x\times\sqrt{2} x=10\times x^2$]

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

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

Hence, $x^{2}+6 \sqrt{2} x+10= (x+5 \sqrt{2})(x+\sqrt{2})$.

Tutorialspoint

Updated on: 10-Oct-2022

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