Question

simplify the following : (√3 + √2)^2​

Answer 1

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(√3 + √2)²

Using the identity

(a+b)² = a²+b²+2ab

Here,

a=√3

b=√2

So,

(√3)² + (√2)² + 2 (√3×√2)

=3 + 2 + 2 (√6)

=3 + 2 + 2√6

Answer 2

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

We know that :-

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

$\implies{( \sqrt{3} + \sqrt{2} )}^{2} = { (\sqrt{3} )}^{2} + { (\sqrt{2} )}^{2} +( 2 \times \sqrt{3} \times \sqrt{2})$

$\implies{( \sqrt{3} + \sqrt{2} )}^{2} =3 + 2 +2\sqrt{6}$

$\implies{( \sqrt{3} + \sqrt{2} )}^{2} =5+2\sqrt{6}$

Answer :

$5+2\sqrt{6}$

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

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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