Calculate (√100 - √9)² ÷ 7: Order of Operations with Square Roots

Previously mentioned in the order of arithmetic operations, exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the root terms inside the parentheses first) :

$(\sqrt{100}-\sqrt{9})^2:7 = (10-3)^2:7 =7^2:7=\frac{7^2}{7}$where in the second step we simplified the expression in parentheses, and in the next step we wrote the division operation as a fraction,

Next we'll calculate the value of the numerator by performing the exponentiation, and in the next step we'll perform the division (essentially reducing the fraction):

$\frac{7^2}{7} =\frac{\not{49}}{\not{7}}=7$Therefore the correct answer is answer A.