The value of `sqrt(19.36) + sqrt(0.1936) + sqrt(0.001936) + sqrt(0.00001936)` is :

Options

A. 4.8484
B. 4.8694
C. 4.8884
D. 4.8234

Answer

To solve the expression \( \sqrt{19.36} + \sqrt{0.1936} + \sqrt{0.001936} + \sqrt{0.00001936} \), we will calculate each square root step by step.

### Step 1: Calculate \( \sqrt{19.36} \)

To find \( \sqrt{19.36} \):
- Recognize that \( 19.36 = 4.4^2 \).
- Therefore, \( \sqrt{19.36} = 4.4 \).

**Hint for Step 1:** Look for perfect squares or use a calculator to find the square root.

### Step 2: Calculate \( \sqrt{0.1936} \)

To find \( \sqrt{0.1936} \):
- Recognize that \( 0.1936 = 0.44^2 \).
- Therefore, \( \sqrt{0.1936} = 0.44 \).

**Hint for Step 2:** Remember that the square root of a decimal can often be found by taking the square root of the whole number and adjusting the decimal point accordingly.

### Step 3: Calculate \( \sqrt{0.001936} \)

To find \( \sqrt{0.001936} \):
- Recognize that \( 0.001936 = 0.044^2 \).
- Therefore, \( \sqrt{0.001936} = 0.044 \).

**Hint for Step 3:** Again, look for the pattern in the decimal and how it relates to the square of smaller numbers.

### Step 4: Calculate \( \sqrt{0.00001936} \)

To find \( \sqrt{0.00001936} \):
- Recognize that \( 0.00001936 = 0.0044^2 \).
- Therefore, \( \sqrt{0.00001936} = 0.0044 \).

**Hint for Step 4:** Keep track of how many decimal places you are moving when finding the square root of very small numbers.

### Step 5: Combine all the results

Now, we can sum all the square roots calculated:
\[ \sqrt{19.36} + \sqrt{0.1936} + \sqrt{0.001936} + \sqrt{0.00001936} = 4.4 + 0.44 + 0.044 + 0.0044 \]

### Step 6: Perform the addition

Calculating the sum:
\[ 4.4 + 0.44 = 4.84 \]
\[ 4.84 + 0.044 = 4.884 \]
\[ 4.884 + 0.0044 = 4.8884 \]

Thus, the final answer is:
\[ \sqrt{19.36} + \sqrt{0.1936} + \sqrt{0.001936} + \sqrt{0.00001936} = 4.8884 \]

**Final Answer:** \( 4.8884 \)