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Simplify each of the following expressions:
(i) 
(3+sqrt3)(2+sqrt2)
(ii) 
(3+sqrt3)(3-sqrt3)
(iii) 
(sqrt5+sqrt2)^(2)
(iv) 
(sqrt5-sqrt2)(sqrt5+sqrt2)

Recall, 
pi is defined as the ratio of the circumference 
(syy) of a circ

22. Simplify each of the following expressions:\newline(i) (3+3)(2+2) (3+\sqrt{3})(2+\sqrt{2}) \newline(ii) (3+3)(33) (3+\sqrt{3})(3-\sqrt{3}) \newline(iii) (5+2)2 (\sqrt{5}+\sqrt{2})^{2} \newline(iv) (52)(5+2) (\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}) \newlineRecall, π \pi is defined as the ratio of the circumference (syy) (s y y) of a circ

Full solution

Q. 22. Simplify each of the following expressions:\newline(i) (3+3)(2+2) (3+\sqrt{3})(2+\sqrt{2}) \newline(ii) (3+3)(33) (3+\sqrt{3})(3-\sqrt{3}) \newline(iii) (5+2)2 (\sqrt{5}+\sqrt{2})^{2} \newline(iv) (52)(5+2) (\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}) \newlineRecall, π \pi is defined as the ratio of the circumference (syy) (s y y) of a circ
  1. Distribute and Multiply: (i) Multiply (3+3)(2+2)(3+\sqrt{3})(2+\sqrt{2}) using the distributive property.\newline(3+3)(2+2)=3×2+3×2+3×2+3×2(3+\sqrt{3})(2+\sqrt{2}) = 3\times 2 + 3\times\sqrt{2} + \sqrt{3}\times 2 + \sqrt{3}\times\sqrt{2}\newline=6+32+23+6= 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}
  2. Difference of Squares: (ii) Multiply (3+3)(33)(3+\sqrt{3})(3-\sqrt{3}) using the difference of squares formula.\newline(3+\sqrt{3})(3-\sqrt{3}) = 3^2 - (\sqrt{3})^2\(\newline= 9 - 3\newline= 6\)
  3. Square Formula: (iii) Square (5+2)(\sqrt{5}+\sqrt{2}) using the formula (a+b)2=a2+2ab+b2.(a+b)^2 = a^2 + 2ab + b^2.\newline(\sqrt{5}+\sqrt{2})^2 = (\sqrt{5})^2 + 2\cdot\sqrt{5}\cdot\sqrt{2} + (\sqrt{2})^2\(\newline= 5 + 2\sqrt{10} + 2\newline= 7 + 2\sqrt{10}\)
  4. Difference of Squares: (iv) Multiply (52)(5+2)(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}) using the difference of squares formula.\newline(\sqrt{\(5\)}-\sqrt{\(2\)})(\sqrt{\(5\)}+\sqrt{\(2\)}) = (\sqrt{\(5\)})^\(2 - (\sqrt{22})^22\newline= 55 - 22\newline= 33

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