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Lesson: 9.4b Multiplication with Radicals
Question 1 of 7, Step 1 of 1
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Correct
Multiply and simplify the following radical expressions.
$(\sqrt{6} + 1) (\sqrt{6} + 1)$

Answer

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Answer

Final Answer: $7 + 2 \sqrt{6}$

Steps

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

Step 3 ：In this case, $a = \sqrt{6}$ and $b = 1$

Step 4 ：So we need to calculate $a^{2} + 2 a b + b^{2}$

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: $7 + 2 \sqrt{6}$