Finding the square root of a decimal can look difficult at first, especially when the number is written as 0.64. However, a simple decimal-to-fraction trick makes the calculation quick and easy.
In this guide, we will use √0.64 as an example. You will learn how to solve it mentally, how to convert the decimal into a fraction, and how to use the same trick with other decimals.
The Quick Answer
To check the answer, multiply 0.8 by itself:
Because the result matches the original number, the principal square root of 0.64 is 0.8.
The Decimal-to-Fraction Square Root Trick
The number 0.64 has two digits after the decimal point, so it can be written as a fraction over 100:
Now take the square root of the fraction:
Since √64 = 8 and √100 = 10, the expression becomes:
This is the key pattern: convert the decimal into a fraction, simplify the square root, and convert the result back into a decimal.
A Faster Mental Math Method
You can also solve √0.64 without writing every step. First, recognize that 64 is a perfect square:
Because 0.64 has two decimal places, the square root has one decimal place in this perfect-square example. The square root of 64 is 8, so the answer is:
Always verify the result by squaring it:
More Examples Using the Same Trick
The same strategy works for many common decimals:
| Problem | Fraction form | Calculation | Answer |
|---|---|---|---|
| √0.09 | 9/100 | 3/10 | 0.3 |
| √0.25 | 25/100 | 5/10 | 0.5 |
| √0.36 | 36/100 | 6/10 | 0.6 |
| √0.49 | 49/100 | 7/10 | 0.7 |
| √0.81 | 81/100 | 9/10 | 0.9 |
| √1.44 | 144/100 | 12/10 | 1.2 |
For example:
How to Handle Decimals with Four Places
The method also works when a decimal has four digits after the decimal point. For example:
The important idea is that square roots reduce the number of decimal places by half when the decimal represents a perfect square.
Common Mistakes to Avoid
One common mistake is to assume that √0.64 equals 0.32 by simply dividing the number by two. A square root is not the same as dividing by two. Instead, it asks: Which number multiplied by itself gives 0.64? Since 0.8 × 0.8 = 0.64, the answer is 0.8.
Another mistake is placing the decimal point incorrectly. Always check your answer by multiplying it by itself. This quick verification step is useful during homework, quizzes, and standardized test practice.
It is also important to distinguish between the square-root symbol and an equation. The expression √0.64 has the principal answer 0.8. If you solve x2 = 0.64, the complete answer is x = ±0.8.
Practice These Problems
Try solving these problems without a calculator:
- √0.04
- √0.16
- √0.25
- √0.49
- √2.25
Answer Key
- √0.04 = 0.2
- √0.16 = 0.4
- √0.25 = 0.5
- √0.49 = 0.7
- √2.25 = 1.5
Final Takeaway
To find the square root of a decimal quickly, look for a perfect-square pattern. Rewrite the decimal as a fraction over 10, 100, or 10,000, take the square root of the numerator and denominator, and simplify the result.
Once you understand this pattern, square roots of decimals become faster and less intimidating. Save this Maths Tricks guide for your next homework session, test review, or mental-math practice.
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