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Answer
The expression simplifies to \( 2\sqrt{30} + 4\sqrt{5} \).
Solution
We start with the expression:
2√5(√6 + 2)
Distribute 2√5 to both terms inside the parentheses:
= 2√5·√6 + 2√5·2
Simplify each term:
2√5·√6 = 2√(5×6) = 2√30
2√5·2 = 4√5
Thus, the expression becomes:
2√30 + 4√5
This is the simplified form.
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Simplify this solution The Deep Dive
To simplify \( 2 \sqrt{5}(\sqrt{6}+2) \), start by using the distributive property. Multiply \( 2 \sqrt{5} \) by each term inside the parentheses: 1. First, calculate \( 2 \sqrt{5} \cdot \sqrt{6} \), which gives \( 2 \sqrt{30} \) because \( \sqrt{5} \cdot \sqrt{6} = \sqrt{30} \). 2. Next, compute \( 2 \sqrt{5} \cdot 2 \), resulting in \( 4 \sqrt{5} \). Putting it all together, you have \( 2 \sqrt{5}(\sqrt{6}+2) = 2 \sqrt{30} + 4 \sqrt{5} \). So, the simplified expression is: \[ 2 \sqrt{30} + 4 \sqrt{5} \]
