Question

simplify the following expression completely.
$left(\sqrt{7} - \sqrt{4}\
ight)^2$
a $11 - 2\sqrt{7}$
b $3$
c $11$
d $3 - 4\sqrt{7}$
e $11 - 4\sqrt{7}$

Explanation:

Step1: Recall the square of a binomial formula

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a=\sqrt{7}\) and \(b = \sqrt{4}\).

Step2: Simplify \(\sqrt{4}\)

We know that \(\sqrt{4}=2\), so the expression becomes \((\sqrt{7}-2)^2\).

Step3: Apply the binomial square formula

Using the formula \((a - b)^2=a^2-2ab + b^2\) with \(a = \sqrt{7}\) and \(b = 2\):

• Calculate \(a^2\): \((\sqrt{7})^2=7\)
• Calculate \(-2ab\): \(-2\times\sqrt{7}\times2=- 4\sqrt{7}\)
• Calculate \(b^2\): \(2^2 = 4\)

Step4: Combine the terms

Add the three terms together: \(7-4\sqrt{7}+4\). Combine the constant terms \(7 + 4=11\), so the simplified expression is \(11-4\sqrt{7}\).

Answer:

E. \(11 - 4\sqrt{7}\)