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Find the positive square root of [tex]7+2\sqrt{6}[/tex].
To find the positive square root of the expression [tex]\( 7 + 2 \sqrt{6} \)[/tex], we proceed as follows:
1. Identify the expression: We start with the expression [tex]\( 7 + 2 \sqrt{6} \)[/tex].
2. Evaluate the expression under the square root: The expression inside the square root is already in its simplest form, so we simply note that it is [tex]\( 7 + 2 \sqrt{6} \)[/tex].
3. Find its positive square root: The goal is to find the value of [tex]\( \sqrt{7 + 2 \sqrt{6}} \)[/tex].
4. Calculate: After evaluating, we get that the positive square root of [tex]\( 7 + 2 \sqrt{6} \)[/tex] is approximately [tex]\( 3.449489742783178 \)[/tex].
Therefore, the positive square root of [tex]\( 7 + 2 \sqrt{6} \)[/tex] is approximately [tex]\( 3.449489742783178 \)[/tex].
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