Question

the square root function
quiz complete
1 2 3 4 5 6
the factor tree for 1,764 is shown. what is the simplest form of \\(\sqrt{1764}\\)?
(image of factor tree: 1,764 splits into 2 and 882; 882 splits into 2 and 441; 441 splits into 9 and 49; 9 splits into 3 and 3; 49 splits into 7 and 7)
options: 21, 42, \\(3^2(7^2)\\), \\(2^2(3^2)(7^2)\\)
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Explanation:

Step1: Find prime factors of 1764

From factor tree, \(1764 = 2\times2\times3\times3\times7\times7\)

Step2: Rewrite as squares

\(1764=(2\times3\times7)^2 = 42^2\)

Step3: Take square root

\(\sqrt{1764}=\sqrt{42^2}=42\)

Answer:

42