Question

find the square of √5-2 ​

Answer 1

Answer:

(a-b)^2 = a^2 - 2ab + b^2

(root5 - 2)^2 = (root 5)^2 - 2 * root 5 * 2 + 2^2

                  = 5 - 4root5 + 4

                  = 9 - 4 * root5

Answer 2

$\displaystyle\sf{We \:have \:to \:find \: (\sqrt5-2)^2$

${\displaystyle\sf{This\:is\:in\:the\:form\:(a-b)^2$

$\boxed{\displaystyle\sf{(a-b)^2=a^2-2ab+b^2}}$

${\displaystyle\sf{Here,$

• ${\displaystyle\sf{a=\sqrt5$

• ${\displaystyle\sf{b=2$

${\displaystyle\sf{Applying\:the\:values\:to\:the\:equation\:,$

$\displaystyle\sf{(\sqrt5-2)^2=(\sqrt5)^2-(2\times\sqrt5\times2)+(2)^2$

$\displaystyle\sf{\implies (\sqrt5-2)^2=5-4\sqrt5+4$

$\implies{\displaystyle\sf{(\sqrt5-2)^2=9-4\sqrt5$

$\boxed{{\displaystyle\sf{(\sqrt5-2)^2=9-4\sqrt5}}}$