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Readme [11.4K]
3 years ago
7

Can anyone please explain this question to me?(2√5+3√6)²​

Mathematics
2 answers:
iogann1982 [59]3 years ago
7 0

\displaystyle \huge \boxed{\mathfrak{Question} \downarrow}

\displaystyle\large \bf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\large \sf(  2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }

  • Use the algebraic identify \sf\left(a+b\right)^{2}=a^{2}+2ab+b^{2}to expand \sf\left(2\sqrt{5}+3\sqrt{6}\right)^{2}.

\large \sf \: 4\left(\sqrt{5}\right)^{2}+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2}

  • The square of \sf\sqrt{5} is 5.

\large \sf4\times 5+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2}

  • Multiply 4 and 5 to get 20.

\large \sf20+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2}

  • To multiply \sf\sqrt{5} and \sf\sqrt{6}, multiply the numbers under the square root.

\large \sf20+12\sqrt{30}+9\left(\sqrt{6}\right)^{2}

  • The square of \sf\sqrt{6} is 6.

\large \sf20+12\sqrt{30}+9\times 6

  • Multiply 9 and 6 to get 54.

\large \sf20+12\sqrt{30}+54

  • Add 20 and 54 to get 74.

\large  \boxed{\bf12 \sqrt{30} + 74 = 139.72..}

andrey2020 [161]3 years ago
7 0

Step-by-step explanation:

<h3>(2√5+3√6)^2</h3>

<h3>(x+y) ^2= x^2+2xy+y^2, </h3>

<h3> (x = 2√5) , (y =3√6)</h3>

<h3>(2√5)^2 + 2(2√5)(3√6) + (3√6)^2</h3>

<h3>4(5) + 12√30 + 9(6)</h3>

<h3>20 + 12√30 + 54</h3>

<h3>= 74 + 12√30 or 74 + 65.72 = 139.72 </h3>

<h3>Hope, It helps You</h3>
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