Question

question
express the product \\((\sqrt{2} + 3)(\sqrt{2} + 3)\\) in simplest form.

Explanation:

Step1: Recognize the form as a square of a binomial

The expression \((\sqrt{2} + 3)(\sqrt{2} + 3)\) is the same as \((\sqrt{2} + 3)^2\). The formula for squaring a binomial \((a + b)^2\) is \(a^2 + 2ab + b^2\), where \(a=\sqrt{2}\) and \(b = 3\).

Step2: Apply the binomial square formula

First, calculate \(a^2\): \((\sqrt{2})^2=2\).
Then, calculate \(2ab\): \(2\times\sqrt{2}\times3 = 6\sqrt{2}\).
Next, calculate \(b^2\): \(3^2 = 9\).

Step3: Combine the terms

Add the three terms together: \(2+6\sqrt{2}+9\).
Combine the constant terms: \(2 + 9=11\). So the expression becomes \(11 + 6\sqrt{2}\).

Answer:

\(11 + 6\sqrt{2}\)