Question

Simplify : (1 + √8)(1 - 2√2)​

Answer 1

Given :

An expression $(1+\sqrt{8} )(1-2\sqrt{2} )$.

To find :

The value of the expression.

Step-by-step explanation:

• The value of the expression can be found by following the steps.
• $\sqrt{8}$ can be written as $2\sqrt{2}$
• Therefore, the expression can be written as

       $(1+2\sqrt{2} )(1-2\sqrt{2} )$

• The formula used is

       $(a-b)(a+b)=a^{2} -b^{2}$

• Substitute the value in the given equation.

       $(1+2\sqrt{2} )(1-2\sqrt{2} ) = [(1)^{2} -(2\sqrt{2} )^{2} ]$

• Remove the brackets

       $(1+2\sqrt{2} )(1-2\sqrt{2} )=1-[(2)^{2} (\sqrt{2} )^{2} ]$

• Square the values

       $(1+2\sqrt{2} )(1-2\sqrt{2} )=1-(4)(2)$

• Sum it all up

       $(1+2\sqrt{2} )(1-2\sqrt{2} )=1-8$

• Final value is

       $(1+2\sqrt{2} )(1-2\sqrt{2} )=-7$

Final answer :

The value of the expression $(1+\sqrt{8} )(1-2\sqrt{2} )$ is $-7$.