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

Instead of manipulating the expression symbolically from the start, this can be checked by plugging in a concrete positive value for $R$ and following the same instructions.

1. Let $R = 2$.
2. Multiply by 8: $8 \times 2 = 16$.
3. Square the result: $16^2 = 256$.
4. Divide by 4: $\frac{256}{4} = 64$.
5. Take the square root: $\sqrt{64} = 8$.
6. So $Q = 8$ when $R = 2$. Checking the options with $R=2$: option (2), $4R$, gives $4 \times 2 = 8$, which matches exactly. Option (1) gives $3R = 6$, option (3) gives $7R = 14$, and option (4) gives $9R = 18$, none of which equal the computed value of 8.

Since $Q = 4R$ holds for this test value, and the algebraic derivation gives the same general relationship, $Q$ must equal $4R$ for any positive $R$.

\[\boxed{Q = 4R}\]