The value of 64y2z3 is
The Correct Answer and Explanation is:
The correct answer is 6.
To solve the expression √64 − 2, begin by evaluating the square root. The square root of 64 is the number that, when multiplied by itself, gives 64. This number is 8 because 8 × 8 equals 64.
After calculating the square root, subtract 2 from the result: 8 − 2 = 6
So, √64 − 2 equals 6.
This question assesses your understanding of two fundamental mathematical operations: square roots and subtraction. The square root symbol (√) indicates the principal square root, which is the non-negative root. In this case, √64 asks for the positive number whose square is 64. Since 8 × 8 = 64, the square root of 64 is 8.
Next comes subtraction. This arithmetic operation finds the difference between numbers. Once we determined that √64 = 8, subtracting 2 from 8 gives the final result: 6.
This type of problem highlights how essential it is to understand order of operations. The square root must be evaluated before the subtraction. If the operations were reversed or misinterpreted, one might mistakenly subtract first, resulting in an incorrect solution.
Moreover, this problem is a good example of the layered nature of mathematical expressions. It requires recognizing the components of the expression, applying the appropriate operations in sequence, and confirming that the result makes sense in context.
These foundational skills are crucial not only in simple arithmetic but also in advanced algebra, calculus, and applied sciences. Square roots appear in formulas involving area, standard deviation, quadratic equations, and physical laws. Subtraction underlies concepts like rate of change and net value.
In summary, the accurate evaluation of √64 − 2 results in 6. This process reflects a clear understanding of roots, arithmetic, and procedural accuracy. Mastering these basics paves the way for handling more complex mathematical challenges with confidence
