Expand and simplify $\newline$ $(2+\sqrt{2})(3+\sqrt{8})$ $\newline$ Give your answer in the form $a+b \sqrt{2}$ , where $a$ and $b$ are integers. $\newline$ ( $4$ marks) $\newline$ $\square$ $\newline$ Submit Answer

Full solution

Q. Expand and simplify

\newline

(2+\sqrt{2})(3+\sqrt{8})

\newline

Give your answer in the form

a+b \sqrt{2}

, where

a

and

b

are integers.

\newline

(

4

marks)

\newline

\square

\newline

Submit Answer

Simplify $\sqrt{8}$ : First, let's simplify $\sqrt{8}$ to make the multiplication easier. $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}$ .
Expand using distributive property: Now, let's use the distributive property to expand $(2+\sqrt{2})(3+2\sqrt{2})$ . $(2+\sqrt{2})(3+2\sqrt{2}) = 2\cdot 3 + 2\cdot 2\sqrt{2} + \sqrt{2}\cdot 3 + \sqrt{2}\cdot 2\sqrt{2}$ .
Perform multiplication for each term: Perform the multiplication for each term. $2 \times 3 = 6$ , $2 \times 2\sqrt{2} = 4\sqrt{2}$ , $\sqrt{2} \times 3 = 3\sqrt{2}$ , and $\sqrt{2} \times 2\sqrt{2} = 2 \times 2$ .
Add results: Add the results together. $\newline$ $6 + 4\sqrt{2} + 3\sqrt{2} + 2\times2 = 6 + 7\sqrt{2} + 4$ .
Combine like terms: Combine like terms and simplify. $\newline$ $6 + 4 + 7\sqrt{2} = 10 + 7\sqrt{2}$ .