Question

\(\sqrt{100} - \sqrt{36}\) =

• A. 4
• B. 8
• C. 16
• D. 64
• E. 256

Hint:

A common mistake is to subtract the numbers inside the square roots first: \(\sqrt{100 - 36} = \sqrt{64} = 8\). This is incorrect. Remember that \(\sqrt{a} - \sqrt{b} \neq \sqrt{a-b}\). You must evaluate each square root separately before performing addition or subtraction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves finding the principal square roots of two numbers and then performing subtraction.
Step 2: Detailed Explanation:
First, we evaluate each square root individually.
The principal square root of 100 is the number that, when multiplied by itself, equals 100.
\[ \sqrt{100} = 10 \quad (\text{since } 10 \times 10 = 100) \] The principal square root of 36 is the number that, when multiplied by itself, equals 36.
\[ \sqrt{36} = 6 \quad (\text{since } 6 \times 6 = 36) \] Now, we perform the subtraction:
\[ \sqrt{100} - \sqrt{36} = 10 - 6 = 4 \] Step 3: Final Answer:
The result of the expression is 4. This corresponds to option (A).