Question

Simplify (5-sqrt3)^2

Answer 1

we have to simplify :-

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

we know that :-

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

Therefore now :-

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

$\implies{(5 - \sqrt{3} )}^{2} = {25} + 3 - 10\sqrt{3}$

$\implies{(5 - \sqrt{3} )}^{2} = 28- 10\sqrt{3}$

$\implies{(5 - \sqrt{3} )}^{2} = 2( 14- 5\sqrt{3})$

Answer :

${(5 - \sqrt{3} )}^{2} = 2( 14- 5\sqrt{3})$

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$\large\bf\blue{Additional-Information}$

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

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

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

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

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

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

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