Question

Simplify each of the following expressions
I. ( 3+√3) (2+√2)
II. (3+√3) (3-√3)
III. (√5+√2)²
IV.(√5-√2) (√5+√2)

Answer 1

Heya !!



(1) ( 3 + ✓3 ) ( 2 + ✓2 )



=> 3 ( 2 + ✓2 ) + ✓3 ( 2 + ✓2 )




=> 6 + 3✓2 + 2✓3 + ✓6 [ Answer ]



(2) ( 3 + ✓3 ) ( 3 - ✓3 )



=> (3)² - (✓3)²



=> 9 - 3


=> 6 [ Answer ]



(3) ( ✓5 + ✓2 )²


=> (✓5)² + (✓2)² + 2 × ✓5 × ✓2


=> 5 + 2 + 2✓10




=> 7 + 2✓10 [ Answer ]



(4) ( ✓5 - ✓2 ) ( ✓5 + ✓2 )



=> (✓5)² - (✓2)²


=> 5 - 2


=> 3 [ Answer ]

Answer 2

I. $( 3+\sqrt{3} ) (2+\sqrt{2} )$

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

II. $(3+\sqrt{3} ) (3-\sqrt{3} )$

We know that,

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

$\therefore 3^{2} -(\sqrt{3} )^{2}=9-3=6$

III. $(\sqrt{5} +\sqrt{2})^{2}$

We know that,

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

$\therefore (\sqrt{5})^{2} +(\sqrt{2})^{2} + 2\times \sqrt{5}\times \sqrt{2}=5+2+2\sqrt{10} =7+2\sqrt{10}$

IV. $(\sqrt{5} -\sqrt{2} ) (\sqrt{5}+\sqrt{2})$

We know that,

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

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

#SPJ2