(2root5+3root2)square ?

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(2root5+3root2)square ?

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Answer 1 · 2018-06-22T15:36:37

$38 + 12 \sqrt{10}$ $38+12sqrt(10)$

Explanation:

To format this write:

hash ( 2sqrt(5)+3sqrt(2) )^2 hash

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

Write as:

$(2 \sqrt{5} + 3 \sqrt{2}) (2 \sqrt{5} + 3 \sqrt{2})$ $color( blue)((2sqrt(5)+3sqrt(2))color(green)(( 2sqrt(5)+3sqrt(2))$

Multiply everything inside the green bracket by everything in the blue.

$2 \sqrt{5} [\frac{.}{.} 2 \sqrt{5} + 3 \sqrt{2} \frac{.}{.}] ddddd + 3 \sqrt{2} [\frac{.}{.} 2 \sqrt{5} + 3 \sqrt{2} \frac{.}{.}]$ $color(green)( color(blue)(2sqrt(5)) [color(white)(./.)2sqrt(5)+3sqrt(2)color(white)(./.)] color(white)("ddddd")color(blue)(+3sqrt(2)) [color(white)(./.)2sqrt(5) +3sqrt(2)color(white)(./.)] )$

Notice the + followed the $+ 3 \sqrt{2}$ $color(blue)(+3sqrt(2))$

${(2 \sqrt{5})}^{2} + 2 \sqrt{5} \times 3 \sqrt{2} dddd + 2 \sqrt{5} \times 3 \sqrt{2} + {(3 \sqrt{2})}^{2}$ $(2sqrt(5))^2 +2sqrt(5) xx3sqrt(2) color(white)("dddd") +2sqrt(5) xx3sqrt(2) + (3sqrt(2))^2$

Lets introduce a pairs of bracket to group things.

$[{(2 \sqrt{5})}^{2}] + [\frac{2}{2} 2 \sqrt{5} \times 3 \sqrt{2} dddd + 2 \sqrt{5} \times 3 \sqrt{2} d] + [{(3 \sqrt{2})}^{2}]$ $[(2sqrt(5))^2] +[ color(white)(2/2)2sqrt(5) xx3sqrt(2) color(white)("dddd") +2sqrt(5) xx3sqrt(2) color(white)("d")] + [(3sqrt(2))^2]$

We can factor out the $2 \sqrt{5}$ $2sqrt(5)$

$[4 \times 5] ddd + dd 2 \sqrt{5} [\frac{2}{2} 3 \sqrt{2} dddd + 3 \sqrt{2} d] ddddd + [9 \times 2]$ $[4xx5] color(white)("ddd")+ color(white)("dd")2 sqrt(5)[ color(white)(2/2)3sqrt(2) color(white)("dddd") +3sqrt(2) color(white)("d")] color(white)("ddddd")+ [9xx2]$

$dd 20 dddd + ddddddddd [2 \sqrt{5} \times 6 \sqrt{2}] ddddddddd + 18$ $color(white)("dd")20 color(white)("dddd")+ color(white)("ddddddddd")[2sqrt5 xx 6sqrt2] color(white)("ddddddddd")+18$

$d$ $color(white)("d")$
$d$ $color(white)("d")$

$dddddddddddddddddd 20 + 18 + 12 \sqrt{5 \times 2}$ $color(white)("dddddddddddddddddd")20+18+12sqrt(5xx2)$

$dddddddddddddddddddd 38 + 12 \sqrt{10}$ $color(white)("dddddddddddddddddddd")38+12sqrt(10)$

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(2root5+3root2)square ?

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