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√(5)+3√(6)\right)^(2)`.

`\large \sf \: 4\left(√(5)\right)^(2)+12√(5)√(6)+9\left(√(6)\right)^(2)`

• The square of
  `\sf√(5)` is 5.

`\large \sf4* 5+12√(5)√(6)+9\left(√(6)\right)^(2)`

• Multiply 4 and 5 to get 20.

`\large \sf20+12√(5)√(6)+9\left(√(6)\right)^(2)`

• To multiply
  `\sf√(5)` and
  `\sf√(6)`, multiply the numbers under the square root.

`\large \sf20+12√(30)+9\left(√(6)\right)^(2)`

• The square of
  `\sf√(6)` is 6.

`\large \sf20+12√(30)+9* 6`

• Multiply 9 and 6 to get 54.

`\large \sf20+12√(30)+54`

• Add 20 and 54 to get 74.

`\large \boxed{\bf12 √(30) + 74 = 139.72..}`