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a) √8 + 2√3 - √27 - √2
= √(4.2) + 2√3 - √(9.3) - √2
= 2√2 + 2√3 - 3√3 - √2
= 2√2 - √2 + 2√3 - 3√3
= √2 - √3
b) 3√6 x 2√8 : 2√3
= 3√6 x 2√(4.2) : 2√3
= 3√6 x 2.2√2 : 2√3
= 3√6 x 4√2 : 2√3
= 12√12 : 2√3
= 12√(4.3) : 2√3
= 12.2√3 : 2√3
= 24√3 : 2√3
= 24 : 2
= 12
c) √8 + 2√2 - (3√3 x √8)
= √(4.2) + 2√2 - (3√3 x √(4.2)
= 2√2 + 2√2 - (3√4 x 2√2)
= 4√2 - 6√8
= 4√2 - 6.√(4.2)
= 4√2 - 6.2√2
= 4√2 - 12√2
= -8√2
d) √27 - 4√2 + 3√8 : √18
= √(9.3) - 4√2 + 3.√(4.2) + √(9.2)
= 3√3 - 4√2 + 3.2√2 + 3√2
= 3√3 - 4√2 + 6√2 + 3√2
= 3√3 + 2√2 + 3√2
= 3√3 + 5√2
2.
a) 2^5 x 16 : 128
= 2^5 x 2^4 : 2^7
= 2^5+4-7
= 2^9-7
= 2²
b) (3^5 x 27²)²
________
(9^10 : 81)²
3^5.2 x 27^2.2
= ______________
9^10.2 : 81²
3^10 x 27^4
= ____________
9^20 : 81²
3^10 x (3^3)^4
= ______________
(3²)^20 : (3^4)²
3^10 x 3^12
= ___________
3^40 : 3^8
3^10+12
= ________
3^40-8
= 3^22+32
= 3^54