Question

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

Answer 1

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

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

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

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

• 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.

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