Question

Q3.Simplify the following:
(i) (5+√7)(2 + √5 )
(ii) (2√3 +6√5 ) (5√2 - 3√3)
(iii) (√11 +√7) (√11 - √7)
(iv) (8√2 + 3√5 ) (3√2 - 6√3)
please solve all question step wise ​

Answer 1

See one by one:-

(i)

$(5 + \sqrt{7} )(2 + \sqrt{5)}$

$= 5 (2 + \sqrt{5} ) + \sqrt{7} (2 + \sqrt{7} )$

$= 10 + 5 \sqrt{5 } + 2 \sqrt{7} + \sqrt{35}$

(ii)

$(2 \sqrt{3} + 6 \sqrt{5} )(5 \sqrt{2} - 3 \sqrt{3} )$

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

$= 10 \sqrt{6} - 18 + 30 \sqrt{10} - 18 \sqrt{15}$

$= 10 \sqrt{6} + 30 \sqrt{10} - 18 \sqrt{15} - 18$

(iii)

$(\sqrt{11} + \sqrt{7} )( \sqrt{11} - \sqrt{7} )$

$= ( \sqrt{11} )^{2} - ( \sqrt{7} )^{2}$

$= 11 - 7 = 4$

(iv)

$(8 \sqrt{2} + 3 \sqrt{5} )(3 \sqrt{2} - 6 \sqrt{3} )$

$= (8 \sqrt{2} (3 \sqrt{2} - 6 \sqrt{3} )+ 3 \sqrt{5} )(3 \sqrt{2} - 6 \sqrt{3} )$

$48 - 48 \sqrt{6} + 9 \sqrt{10} - 18 \sqrt{15}$

Enjoy Maths!!

(SK Study Point Siliguri)