Compare Expressions: Determine the Sign Between (1/25)(5² - 3 + √9) and √25·5·(1/5)

We solve the left side and start from the parentheses:

$5^2=5\times5=25$

We will solve the root exercise using the equation:$\sqrt{a^2}=a$

$\sqrt{9}=\sqrt{3^2}=3$

We arrange the exercise accordingly:

$\frac{1}{25}\times(25-3+3)=$

We solve the exercise in parentheses from left to right:

$\frac{1}{25}\times(22+3)=\frac{1}{25}\times25$

We convert the 25 into a simple fraction, multiply and divide:

$\frac{1}{25}\times\frac{25}{1}=\frac{25}{25}=\frac{1}{1}=1$

We solve the right side:

$\sqrt{25}=\sqrt{5^2}$

We arrange the exercise:

$\sqrt{5^2}\times5\times\frac{1}{5}$

We convert the 5 into a simple fraction and note that it is possible to reduce by 5:

$\sqrt{5^2}\times\frac{5}{1}\times\frac{1}{5}=\sqrt{5^2}\times1$

We solve the root according to the formula:$\sqrt{a^2}=a$

$5\times1=5$

Now we are going to compare the left side with the right side, and it seems that we obtained two different results and therefore the two sides are not equal.