[tex]\displaystyle \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \displaystyle\large \bf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \large \sf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
- Use the algebraic identify [tex]\sf\left(a+b\right)^{2}=a^{2}+2ab+b^{2} [/tex]to expand [tex]\sf\left(2\sqrt{5}+3\sqrt{6}\right)^{2}[/tex].
[tex] \large \sf \: 4\left(\sqrt{5}\right)^{2}+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
- The square of [tex]\sf\sqrt{5}[/tex] is 5.
[tex] \large \sf4\times 5+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
- Multiply 4 and 5 to get 20.
[tex] \large \sf20+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
- To multiply [tex]\sf\sqrt{5}[/tex] and [tex]\sf\sqrt{6}[/tex], multiply the numbers under the square root.
[tex] \large \sf20+12\sqrt{30}+9\left(\sqrt{6}\right)^{2} [/tex]
- The square of [tex]\sf\sqrt{6}[/tex] is 6.
[tex] \large \sf20+12\sqrt{30}+9\times 6 [/tex]
- Multiply 9 and 6 to get 54.
[tex] \large \sf20+12\sqrt{30}+54 [/tex]
[tex] \large \boxed{\bf12 \sqrt{30} + 74 = 139.72..}[/tex]
