QuestionJuly 20, 2025

Simplify: (7+2sqrt (3))^2 square

Simplify: (7+2sqrt (3))^2 square
Simplify:
(7+2sqrt (3))^2
square

Solution
3.4(249 votes)

Answer

61 + 28\sqrt{3} Explanation 1. Apply the Binomial Theorem Use **(a+b)^2 = a^2 + 2ab + b^2** with a = 7 and b = 2\sqrt{3}. 2. Calculate a^2 7^2 = 49 3. Calculate 2ab 2 \times 7 \times 2\sqrt{3} = 28\sqrt{3} 4. Calculate b^2 (2\sqrt{3})^2 = 4 \times 3 = 12 5. Sum the results 49 + 28\sqrt{3} + 12 = 61 + 28\sqrt{3}

Explanation

1. Apply the Binomial Theorem<br /> Use **$(a+b)^2 = a^2 + 2ab + b^2$** with $a = 7$ and $b = 2\sqrt{3}$.<br /><br />2. Calculate $a^2$<br /> $7^2 = 49$<br /><br />3. Calculate $2ab$<br /> $2 \times 7 \times 2\sqrt{3} = 28\sqrt{3}$<br /><br />4. Calculate $b^2$<br /> $(2\sqrt{3})^2 = 4 \times 3 = 12$<br /><br />5. Sum the results<br /> $49 + 28\sqrt{3} + 12 = 61 + 28\sqrt{3}$
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