Question

simplify 1/7+3root2​

Answer 1

hope its helpfull for u

Answer 2

Answer:

$\dfrac{1}{7+3\sqrt{2}}=\dfrac{7-3\sqrt{2}}{31}\quad \left(\mathrm{Decimal:\quad }\:0.08895\dots \right)$

Step-by-step explanation:

​$\dfrac{1}{7+3\sqrt{2}}$

$\mathrm{Multiply\:by\:the\:conjugate}\:\dfrac{7-3\sqrt{2}}{7-3\sqrt{2}}$

$=\dfrac{1\cdot \left(7-3\sqrt{2}\right)}{\left(7+3\sqrt{2}\right)\left(7-3\sqrt{2}\right)}$

$\mathrm{Simplify\:the\:numerator}$

$1\cdot \left(7-3\sqrt{2}\right)=7-3\sqrt{2}$

$\mathrm{Simplify\:the\:denominator}$

$\left(7+3\sqrt{2}\right)\left(7-3\sqrt{2}\right)$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}\left(a+b\right)\left(a-b\right)=a^2-b^2$ $a=7,\:b=3\sqrt{2}$

$=7^2-\left(3\sqrt{2}\right)^2$

$=49-18$

$\mathrm{Subtract\:the\:numbers:}\:49-18=31$

$=31$

$\mathrm{Plug\:in\:the\:numerator\:and\:the\:denominator\:together}$

$=\dfrac{7-3\sqrt{2}}{31}$