Question

find the square of 3+2√5
please fast....​

Answer 1

${(3 + 2 \sqrt{5}) }^{2}$

$\boxed{ \tt{(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} }$

Using this identity we will find its solution ;

${(3 + 2 \sqrt{5} )}^{2} \\ \\ = { 3 }^{2} + 2(3)(2 \sqrt{5} ) + {(2 \sqrt{5} )}^{2} \\ \\ = 9 + 12 \sqrt{5} + 4 \times 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 9 + 12 \sqrt{5} + 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \underline{\underline{ 29 + 12 \sqrt{5} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\\ \\ \\ \\ \color{red}{ \bf{Hope \: \: this \: \: helps \: \: you \: !}}$

Answer 2

Answer:

{(3 + 2 \sqrt{5}) }^{2}(3+2

5

)

2

\boxed{ \tt{(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} }

(a+b)

2

=a

2

+2ab+b

2

Using this identity we will find its solution ;

\begin{gathered} {(3 + 2 \sqrt{5} )}^{2} \\ \\ = { 3 }^{2} + 2(3)(2 \sqrt{5} ) + {(2 \sqrt{5} )}^{2} \\ \\ = 9 + 12 \sqrt{5} + 4 \times 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 9 + 12 \sqrt{5} + 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \underline{\underline{ 29 + 12 \sqrt{5} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}

(3+2

5

)

2

=3

2

+2(3)(2

5

)+(2

5

)

2

=9+12

5

+4×5

=9+12

5

+20

=

29+12

5

\begin{gathered} \\ \\ \\ \\ \color{red}{ \bf{Hope \: \: this \: \: helps \: \: you \: !}}\end{gathered}

Hopethishelpsyou!