Understanding the Square Root of a Decimal

The question asks us to find the value of the square root of the decimal number 0.0144. Finding the square root of a decimal involves determining a number which, when multiplied by itself, gives the original decimal number.

Let's break down how to calculate the square root of 0.0144.

Calculating the Square Root of 0.0144

There are a couple of common methods to find the square root of a decimal like 0.0144.

Method 1: Convert Decimal to Fraction

We can convert the decimal 0.0144 into a fraction. The number 0.0144 has 4 decimal places. This means we can write it as:

\(0.0144 = \frac{144}{10000}\)

Now, we need to find the square root of this fraction:

\(\sqrt{0.0144} = \sqrt{\frac{144}{10000}}\)

Using the property of square roots that \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\), we get:

\(\sqrt{\frac{144}{10000}} = \frac{\sqrt{144}}{\sqrt{10000}}\)

We know the square root of 144 is 12 (since \(12 \times 12 = 144\)).

We also know the square root of 10000 is 100 (since \(100 \times 100 = 10000\)).

So, the fraction becomes:

\(\frac{12}{100}\)

Finally, convert this fraction back to a decimal:

\(\frac{12}{100} = 0.12\)

Method 2: Using the Number of Decimal Places

Consider the number without the decimal point, which is 144. Find the square root of 144.

\(\sqrt{144} = 12\)

Now, count the number of decimal places in the original number, 0.0144. There are 4 decimal places.

When you take the square root of a number, the number of decimal places in the result is half the number of decimal places in the original number.

Number of decimal places in 0.0144 = 4

Number of decimal places in \(\sqrt{0.0144}\) = \(\frac{4}{2} = 2\)

So, take the square root of 144, which is 12, and place the decimal point such that there are 2 decimal places. Starting from the right of 12, move the decimal point 2 places to the left.

12 → 1.2 → 0.12

Thus, the square root of 0.0144 is 0.12.

Verifying the Square Root Calculation

To verify our answer, we can multiply the result by itself:

\(0.12 \times 0.12\)

Multiplying 12 by 12 gives 144. Since each of the numbers being multiplied has 2 decimal places, the product will have \(2 + 2 = 4\) decimal places.

\(0.12 \times 0.12 = 0.0144\)

This matches the original number, confirming that 0.12 is indeed the square root of 0.0144.

Comparing with the Options

Let's look at the given options:

• A. 0.12
• B. 0.012
• C. 1.2
• D. 0.0012

Our calculated value is 0.12, which matches option A.

Final Answer for √0.0144

Based on our calculations using both the fraction method and the decimal place method, the value of \(\sqrt{0.0144}\) is 0.12.

Revision Table: Square Root Calculation

Additional Information: Square Roots and Decimals

Understanding square roots of decimals is crucial for quantitative aptitude sections in exams. Here are a few key points:

• The square root symbol is \(\sqrt{\text{ }}\).
• A perfect square decimal is one whose square root is a terminating decimal.
• To estimate the square root of a decimal, you can often look at the integer part or convert it to a fraction.
• Always double-check your answer by squaring the result.

For example, finding the square root of 0.25:

\(\sqrt{0.25} = \sqrt{\frac{25}{100}} = \frac{\sqrt{25}}{\sqrt{100}} = \frac{5}{10} = 0.5\)

Number of decimal places in 0.25 is 2. Half of 2 is 1. \(\sqrt{25} = 5\). With 1 decimal place, it's 0.5.

Understanding how the number of decimal places relates to the square root helps solve these problems quickly.