Question

8.4 add, subtract, and multiply radical expressions
score: 20.8/22 answered: 21/22
question 22
expand and simplify.
$(7 + 3sqrt{5})^2=$
question help: video written example
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Explanation:

Step1: Apply the formula $(a + b)^2=a^{2}+2ab + b^{2}$

Here $a = 7$ and $b=3\sqrt{5}$, so $(7 + 3\sqrt{5})^{2}=7^{2}+2\times7\times3\sqrt{5}+(3\sqrt{5})^{2}$

Step2: Calculate each term

$7^{2}=49$, $2\times7\times3\sqrt{5}=42\sqrt{5}$, and $(3\sqrt{5})^{2}=3^{2}\times(\sqrt{5})^{2}=9\times5 = 45$

Step3: Combine the terms

$49+42\sqrt{5}+45=94 + 42\sqrt{5}$

Answer:

$94 + 42\sqrt{5}$