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)

Distributive Property Simplification: (i) Simplify (3+sqrt3)(2+sqrt2) using the distributive property. (3+sqrt3)(2+sqrt2) = 3*2 + 3*sqrt2 + sqrt3*2 + sqrt3*sqrt2 = 6 + 3sqrt2 + 2sqrt3 + sqrt6Difference of Squares Simplification: (ii) Simplify (3+sqrt3)(3-sqrt3) using the difference of squares formula. (3+sqrt3)(3-sqrt3) = 3^2 - (sqrt3)^2 = 9 - 3 = 6Binomial Expansion Simplification: (iii) Simplify (sqrt5+sqrt2)^(2) using the binomial expansion. (sqrt5+sqrt2)^2 = (sqrt5)^2 + 2*sqrt5*sqrt2 + (sqrt2)^2 = 5 + 2sqrt10 + 2 = 7 + 2sqrt10Difference of Squares Simplification: (iv) Simplify (sqrt5-sqrt2)(sqrt5+sqrt2) using the difference of squares formula. (sqrt5-sqrt2)(sqrt5+sqrt2) = (sqrt5)^2 - (sqrt2)^2 = 5 - 2 = 3The last part of the problem seems to be cut off and unrelated to the simplification tasks. We'll ignore it.

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Math Problems

Algebra 2

Sum of finite series starts from 1

Full solution

Q. Simplify each of the following expressions:

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(i)

(3+\sqrt{3})(2+\sqrt{2})

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(ii)

(3+\sqrt{3})(3-\sqrt{3})

\newline

(iii)

(\sqrt{5}+\sqrt{2})^{2}

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(iv)

(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})

Distributive Property Simplification: (i) Simplify $(3+\sqrt{3})(2+\sqrt{2})$ using the distributive property. $\newline$ $(3+\sqrt{3})(2+\sqrt{2}) = 3\cdot 2 + 3\cdot\sqrt{2} + \sqrt{3}\cdot 2 + \sqrt{3}\cdot\sqrt{2}$ $\newline$ $= 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$
Difference of Squares Simplification: (ii) Simplify $(3+\sqrt{3})(3-\sqrt{3})$ using the difference of squares formula. $\newline$ (3+\sqrt{3})(3-\sqrt{3}) = 3^2 - (\sqrt{3})^2$\newline= 9 - 3 $\newline$ = 6$
Binomial Expansion Simplification: (iii) Simplify $(\sqrt{5}+\sqrt{2})^{2}$ using the binomial expansion. $\newline$ (\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}$
Difference of Squares Simplification: (iv) Simplify $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$ using the difference of squares formula. $\newline$ (\sqrt{$5$}-\sqrt{$2$})(\sqrt{$5$}+\sqrt{$2$}) = (\sqrt{$5$})^\(2 - (\sqrt{ $2$ })^ $2$ $\newline$ = $5$ - $2$ $\newline$ = $3$
Difference of Squares Simplification: (iv) Simplify $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$ using the difference of squares formula. $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}) = (\sqrt{5})^2 - (\sqrt{2})^2$ $= 5 - 2$ $= 3$ The last part of the problem seems to be cut off and unrelated to the simplification tasks. We'll ignore it.