Simplify (√3 + 2√5)²: Step-by-Step Guide

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In summary, the formula for simplifying (√3 + 2√5)² is (a + b)² = a² + 2ab + b², where a and b are the terms within the parentheses. To simplify, use the formula to expand the expression, simplify each term, and combine like terms. The final answer is 19 + 4√15. Simplifying equations like (√3 + 2√5)² is important because it makes them easier to work with and understand, allows for comparison and manipulation, and can reveal patterns or relationships between terms.
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pan90
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How?

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Taken from HiSet free practice test
 

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pan90 said:
How?
Taken from HiSet free practice test
FOIL it out:
\(\displaystyle ( \sqrt{3} + 2 \sqrt{5} ) ^2 = ( \sqrt{3} + 2 \sqrt{5} ) ( \sqrt{3} + 2 \sqrt{5} )\)

\(\displaystyle = ( \sqrt{3} )^2 + \sqrt{3} \cdot 2 \sqrt{5} + 2 \sqrt{5} \cdot \sqrt{3} + (2 \sqrt{5} )^2\)

Can you finish from here?

-Dan
 

FAQ: Simplify (√3 + 2√5)²: Step-by-Step Guide

What is the formula for simplifying (√3 + 2√5)²?

The formula for simplifying (√3 + 2√5)² is (a + b)² = a² + 2ab + b², where a = √3 and b = 2√5.

What is the first step in simplifying (√3 + 2√5)²?

The first step in simplifying (√3 + 2√5)² is to expand the expression using the formula (a + b)² = a² + 2ab + b².

What is the second step in simplifying (√3 + 2√5)²?

The second step in simplifying (√3 + 2√5)² is to simplify the squared terms, which in this case are √3² and (2√5)². This results in 3 and 4(5), which simplifies to 20.

What is the third step in simplifying (√3 + 2√5)²?

The third step in simplifying (√3 + 2√5)² is to simplify the remaining terms, which in this case are 2√3 and 2(2√5). This results in 4√3 and 4(2√5), which simplifies to 8√3 and 8(√5).

What is the final step in simplifying (√3 + 2√5)²?

The final step in simplifying (√3 + 2√5)² is to combine like terms. In this case, we can combine 20, 8√3, and 8(√5) to get the simplified expression of 20 + 8√3 + 8(√5).

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