Q. 244 - Intermediate Algebra

Question

Use the binomial square pattern to simplify ${(3+\sqrt{2})}^2$. Explain all your steps.

Step-by-Step Solution

Answer

By using Binomial square pattern to simplify ${(3+\sqrt{2})}^2$, we get $11+6\sqrt{2}$

Step 1. Given

The expression ${(3+\sqrt{2})}^2$

To simplify using binomial square pattern.

Step 2. Formula for product of binomial pattern

The product of binomial pattern is:

${(a+b)}^2=a^2+2ab+b^2$

Step 3. Simplify the expression

By using the product of binomial pattern:

${(3+\sqrt{2})}^2={\left(3\right)}^2+2\left(3\right)\sqrt{2})+{\left(\sqrt{2}\right)}^2$

               $=9+6\sqrt{2}+2$

               $=11+6\sqrt{2}$