Question

R is a positive number. It is multiplied by 8 and then squared. The square is now divided by 4 and the square root is taken. The result of the square root is Q. What is the value of Q?

• A. 3R
• B. 4R
• C. 7R
• D. 9R

Hint:

Write each operation as an algebraic step in order: multiply by 8, square, divide by 4, then take the square root.

Answer 1

The Correct Option is B

Step 1: Represent the operations algebraically.
Start with \(R\). Multiplying by 8 gives \(8R\).
Step 2: Square the result.
\((8R)^2 = 64R^2\).
Step 3: Divide by 4.
\(\frac{64R^2}{4} = 16R^2\).
Step 4: Take the square root.
\(\sqrt{16R^2} = 4R\), since \(R\) is given to be positive, so the square root is taken as the positive root.
Step 5: Identify Q.
\(Q = 4R\), which matches option (2). Option (1) would come from a mistaken multiplier, and options (3) and (4) are too large and do not follow from the actual sequence of operations described.