the factor tree for 1,764 is shown. what is the simplest form of √1,764? 21 42 3²(7²) 2²(3²)(7²)

Explanation:

Step1: Write 1764 as product of prime - factors

From the factor - tree, $1764 = 2\times2\times3\times3\times7\times7=2^{2}\times3^{2}\times7^{2}$.

Step2: Find the square - root

$\sqrt{1764}=\sqrt{2^{2}\times3^{2}\times7^{2}}$. According to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a,b\geq0$), we have $\sqrt{2^{2}\times3^{2}\times7^{2}}=\sqrt{2^{2}}\times\sqrt{3^{2}}\times\sqrt{7^{2}}$. Since $\sqrt{x^{2}} = x$ for $x\geq0$, then $\sqrt{2^{2}}\times\sqrt{3^{2}}\times\sqrt{7^{2}}=2\times3\times7 = 42$.

Answer:

42