Question

\(\sqrt{110.25} \times \sqrt{0.01} \div \sqrt{0.0025} - \sqrt{420.25}\) is equal to

• A. \(0.75\)
• B. \(0.50\)
• C. \(0.64\)
• D. \(0.73\)

Hint:

Simplify each square root to a decimal first, then apply BODMAS in order: multiply, divide, subtract.

Answer 1

The Correct Option is B

Step 1: Combine the multiplication and division under one root.
Since $\sqrt{a} \times \sqrt{b} \div \sqrt{c} = \sqrt{\frac{ab}{c}}$, rewrite $\sqrt{110.25} \times \sqrt{0.01} \div \sqrt{0.0025}$ as $\sqrt{\frac{110.25 \times 0.01}{0.0025}}$.

Step 2: Work out the fraction inside the root.
$110.25 \times 0.01 = 1.1025$, and $\frac{1.1025}{0.0025} = 441$.

Step 3: Take the square root.
$\sqrt{441} = 21$.

Step 4: Subtract the last root.
The full expression is now $21 - \sqrt{420.25} = 21 - 20.5$.

Step 5: Finish the subtraction.
$21 - 20.5 = 0.5$.

Final Answer:
Combining the roots first gives the same value with less arithmetic. \[ \boxed{0.5} \]