Question

multiply, and then simplify if possible.
$(sqrt{7} - sqrt{5})^2$

Explanation:

Step1: Apply the square formula \((a - b)^2 = a^2 - 2ab + b^2\)

Here \(a=\sqrt{7}\) and \(b = \sqrt{5}\), so \((\sqrt{7}-\sqrt{5})^2=(\sqrt{7})^2-2\times\sqrt{7}\times\sqrt{5}+(\sqrt{5})^2\)

Step2: Simplify each term

We know that \((\sqrt{x})^2=x\) for \(x\geq0\), so \((\sqrt{7})^2 = 7\), \((\sqrt{5})^2=5\), and \(2\times\sqrt{7}\times\sqrt{5}=2\sqrt{35}\) (using \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\))

Step3: Combine the terms

Substitute the simplified terms back: \(7 - 2\sqrt{35}+5\), then combine like terms \(7 + 5=12\), so we get \(12-2\sqrt{35}\)

Answer:

\(12 - 2\sqrt{35}\)