Step-by-step explanation:

Solution :-

i)

Given that

√8 + √2 + 3√5

= √(2×2×2)+√2+3√5

= 2√2+√2+3√5

= 3√2+3√5 or 3(√2+√5)

Therefore,√8+√2+3√5 = 3√2+3√5 or 3(√2+√5)

ii)

Given that

√50 + √35 + √8

= √(2×5×5)+√35+√(2×2×2)

= 5√2+√35+2√2

= 5√2+2√2+√35

= 7√2+√35

Therefore, √50 + √35 + √8 = 7√2+√35

iii)

Given that

7√50 +√37+√12

= 7√(2×5×5)+√37+√(2×2×3)

= 7×5√2+√37+2√3

= 35√2+√37+2√3

Therefore, 7√50 +√37+√12 = 35√2+√37+2√3

Step-by-step explanation:

(i)√8 + √2+ 3√5

=>√(4*2)+√2+3√(4+1)

=>2√2+√2+3(√4+√1)

=>2√2+√2+3(2+√1)

=>2√2+√2+3(3)

=>2√2+√2+(8+1)

=>2√2+√2+(2√2+1)

=>√2(2+1+2)+1

=>√2(5)+1

ii)√50 +√35 +√8

=>√(25*2)+(√25+10)+2√2

=>5√2+5√10+2√2

=>5√2+5√(2*5)+2√2

=>5√2+5(√2*√5)+2√2

=>√2(5+5√5+2)

iii)7√50 +√37 +√12

=>7√(25*2)+√(25+12)+√(8+4)

=>35√2+√(25+8+4)+√(8+4)

=>35√2+(7+2√2)+(2√2+2)

=>√2(35)+7+2√2+2√2+2

=>√2(35+2+2)+9

=>√2(39)+9