Question

6. Simplify the following: i. (5 + 2√7)(5 - 7√3) ii)(3 + √8)(4 + √5)​

Answer 1

Answer:

1)$25+10\sqrt{7}-35\sqrt{3}-14\sqrt21$

2)$12+3\sqrt{5}+8\sqrt{2}+2\sqrt{10}$

Step-by-step explanation:

1)

$(5+2\sqrt{7} )(5-7\sqrt{3} )\\=>{(5)}^{2}+(2\sqrt{7}-7\sqrt{3} ) 5+(2\sqrt{7} )(-7\sqrt{3})$          $Using \: Identity \:\\(x+a)(x+b)=x^{2} +(a+b)x+ab$

$=>25+10\sqrt{7}-35\sqrt{3}-14\sqrt21$

2)

$(3 + \sqrt8)(4+\sqrt{5})\\=>3 (4+\sqrt{5})+ \sqrt8(4+\sqrt{5})\\=>12+3\sqrt{5}+ 4\sqrt8+\sqrt{40}\\=>12+3\sqrt{5}+ 4\sqrt{(2)(2)(2)}+\sqrt{(2)(2)(2)(5)}\\=>12+3\sqrt{5}+ 4\times 2\sqrt{2}+2\sqrt{10}\\=>12+3\sqrt{5}+8\sqrt{2}+2\sqrt{10}$