Question

The square root of the number 10000000000 is

• A. 1000000
• B. 100000
• C. 10000
• D. 10000000

Hint:

The square root of a number with an even number of zeros simply contains half as many zeros. 10 zeros in the question $\rightarrow$ 5 zeros in the answer!

Answer 1

The Correct Option is B

Concept: The square root of a power of 10 is easily found by counting the zeros. For any number $10^{2n}$, the square root is $10^n$. Mathematically, this is based on the exponent rule: $\sqrt{x^a} = x^{a/2}$

Step 1: Counting the Zeros.
Let's look at the given number: 10,000,000,000. Counting the number of zeros after the digit 1: $\text{Number of zeros} = 10$ Therefore, we can write the number in scientific notation as: $10^{10}$

Step 2: Applying the Square Root.
To find the square root, we divide the exponent by 2: $\sqrt{10^{10}} = 10^{(10/2)} = 10^5$ Now, we convert $10^5$ back into standard form. $10^5$ is 1 followed by 5 zeros: $10^5 = 100,000$

Step 3: Verifying with the options.

• Option A: 1,000,000 (6 zeros)
• Option B: 100,000 (5 zeros)
• Option C: 10,000 (4 zeros)
• Option D: 10,000,000 (7 zeros) Option B matches our calculated value of 100,000. Final Answer: Option B