Question

What will be the value of :
$(2+\sqrt{3}) - (2 - \sqrt{3)}$
​

Answer 1

Answer:

${\huge{\pink{↬}}} \:  \: {\huge{\underline{\boxed{\bf{\pink{Answer}}}}}}$

p= √(16+ 8√3) - √(21-12√3)

= √(8( 2+ √3)) - √3 (7 - 4√3)

p² = {√(16 + 8√3) - √(21 - 12√3)}²

= { 16+ 8√3 - 2√(16 + 8√3)√(21 - 12 -√3) +

21-12-√3}

= {37 -4√3 -2 √ {(16 + 8√3)(21-12-√3) } }

= 37-4√3 -2 √{336 -192√3 + 168 √3 - 288} =37-4√3-2 √{48-24√3}

= 37-4√3 -2 √( 24 (2-√3))

= 37-4√3 -4√(6(2-√3))

= 37-4√3-4√(6(2-√3))

= 25

therefore p =√25

= 5 (answer)

Answer 2

Answer

p= √(16+ 8√3) - √(21-12√3)

= √(8( 2+ √3)) - √3 (7 - 4√3)

p² = {√(16 + 8√3) - √(21 - 12√3)}²

= { 16+ 8√3 - 2√(16 + 8√3)√(21 - 12 -√3) +

21-12-√3}

= {37 -4√3 -2 √ {(16 + 8√3)(21-12-√3) } }

= 37-4√3 -2 √{336 -192√3 + 168 √3 - 288} =37-4√3-2 √{48-24√3}

= 37-4√3 -2 √( 24 (2-√3))

= 37-4√3 -4√(6(2-√3))

= 37-4√3-4√(6(2-√3))

= 25

therefore p =√25

= 5 (answer)