Question

if a=5-2√5 then find a^2​

Answer 1

Answer:

$\huge\boxed{a^2=45-20\sqrt5}$

Step-by-step explanation:

$a=5-2\sqrt5\\\\a^2=(5-2\sqrt5)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\a^2=5^2-2(5)(2\sqrt5)+(2\sqrt5)^2\\\\a^2=25-20\sqrt5+(2^2)(\sqrt5)^2\qquad\text{used}\ (ab)^n=a^nb^n\\\\a^2=25-20\sqrt5+4(5)\qquad\text{used}\ (\sqrt{a})^2=a,\ a\geq0\\\\a^2=25-20\sqrt5+20\\\\a^2=45-20\sqrt5$