the factor tree for 3,025 is shown. what is the simplest form of √3,025? 16 55 5²(11²) 5²+(11²)

Explanation:

Step1: Write prime - factorization

From the factor tree, $3025 = 5\times5\times11\times11=5^{2}\times11^{2}$.

Step2: Calculate the square - root

$\sqrt{3025}=\sqrt{5^{2}\times11^{2}}$. According to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 5^{2}$, $b = 11^{2}$), we have $\sqrt{5^{2}\times11^{2}}=\sqrt{5^{2}}\times\sqrt{11^{2}}$. Since $\sqrt{x^{2}}=x$ for non - negative $x$, then $\sqrt{5^{2}}\times\sqrt{11^{2}} = 5\times11=55$.

Answer:

55