25+322=252+322+22532 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; # ...

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Patterns and Mathematics

Simplify 25+3...

Question

Simplify ${(2 \sqrt{5} + 3 \sqrt{2})}^{2}$ .

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Solution

${(2 \sqrt{5} + 3 \sqrt{2})}^{2} = {(2 \sqrt{5})}^{2} + {(3 \sqrt{2})}^{2} + 2 (2 \sqrt{5}) (3 \sqrt{2}) [{(a + b)}^{2} = a^{2} + b^{2} + 2 a b] = 20 + 18 + 12 \sqrt{10} = 38 + 12 \sqrt{10}$

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\frac{7.83 \times 7.83 - 1.17 \times 1.17}{6.66}

{(\sqrt{3} + \sqrt{7})}^{2}

{(\sqrt{5} - \sqrt{3})}^{2}

{(2 \sqrt{5} + 3 \sqrt{2})}^{2}

Simplify each of the following :

(i) $175 \times 175 + 2 \times 175 \times 25 + 25 \times 25$

(ii) $322 \times 322 - 2 \times 322 \times 22 + 22 \times 22$

(iii) $0.76 \times 0.76 + 2 \times 0.76 \times 0.24 + 0.24 \times 0.24$

(iv) $\frac{7.83 \times 7.83 - 1.17 \times 1.17}{6.66}$

32^{2 / 5}

\frac{(2^{2})^{3}}{(3^{2})^{2}}

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