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Lesson: 9.4b Multiplication with Radicals
Question 1 of 7, Step 1 of 1
$0 / 7$
Correct
Multiply and simplify the following radical expressions.
\[
(\sqrt{6}+1)(\sqrt{6}+1)
\]
Answer
Answer
Final Answer: \(\boxed{7 + 2\sqrt{6}}\)
Step 1 ：Given the expression \((\sqrt{6}+1)(\sqrt{6}+1)\)
Step 2 ：We can use the formula for the square of a binomial, which is \((a+b)^2 = a^2 + 2ab + b^2\)
Step 3 ：In this case, \(a = \sqrt{6}\) and \(b = 1\)
Step 4 ：So we need to calculate \(a^2 + 2ab + b^2\)
Step 5 ：Substituting the values of \(a\) and \(b\) into the formula, we get \((\sqrt{6})^2 + 2(\sqrt{6})(1) + (1)^2\)
Step 6 ：Solving this gives us \(6 + 2\sqrt{6} + 1\)
Step 7 ：Simplifying further, we get \(7 + 2\sqrt{6}\)
Step 8 ：Final Answer: \(\boxed{7 + 2\sqrt{6}}\)
