Simplify; \(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
Question 1 Report
Simplify; \(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
Answer Details
To simplify this expression, we can use the distributive property of multiplication and simplify the terms inside the parentheses first:
\(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
= \(\sqrt{2} \times \sqrt{6} + \sqrt{2} \times 2\sqrt{2} - 2\sqrt{3}\)
= \(\sqrt{12} + 2\sqrt{4} - 2\sqrt{3}\)
= \(2\sqrt{3} + 4 - 2\sqrt{3}\)
= \(4\)
Therefore, the simplified expression is 4.
In summary, we can simplify this expression by first using the distributive property to multiply the \(\sqrt{2}\) by the terms inside the parentheses, then simplifying the resulting expression by combining like terms.
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