5.6-Square Roots of Decimals
5.6-Square Roots of Decimals Important Formulae
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Grade 8 → Math → Squares and Square Roots → 5.6-Square Roots of Decimals
5.6 - Square Roots of Decimals
- The square root of a decimal is the value that, when multiplied by itself, gives the decimal.
- For decimals, express the number as a fraction to simplify calculations.
- If $a = 0.25$, then $\sqrt{a} = \sqrt{\frac{25}{100}} = \frac{5}{10} = 0.5$.
- Square roots of decimals can also be found using estimation and approximation.
- Examples: $\sqrt{0.16} = 0.4$, $\sqrt{0.01} = 0.1$.
5.6 - Square Roots of Decimals
The square root of a decimal is a number that, when multiplied by itself, gives the decimal value. Finding the square root of a decimal is similar to finding the square root of a whole number, but it involves extra care due to the decimal point. Let’s delve into the process of calculating the square root of a decimal.
To find the square root of a decimal, follow these steps:
- Step 1: Convert the decimal into a whole number. This can be done by moving the decimal point to the right, converting the decimal into a whole number.
- Step 2: Find the square root of the whole number as if it were an integer.
- Step 3: After finding the square root, place the decimal point in the appropriate position in the result based on how many places the decimal point was moved.
For example, let’s calculate the square root of 0.09.
1. Convert 0.09 into a whole number by moving the decimal point two places to the right: 0.09 = 9 × $10^{-2}$.
2. Find the square root of 9: $\sqrt{9} = 3$.
3. Place the decimal point back: since we moved the decimal point two places, the square root is $0.3$.
Thus, $\sqrt{0.09} = 0.3$.
Another example: Let’s find the square root of 0.0004.
1. Convert 0.0004 into a whole number: 0.0004 = 4 × $10^{-4}$.
2. Find the square root of 4: $\sqrt{4} = 2$.
3. Place the decimal point back: we moved the decimal point four places, so the square root is $0.02$.
Thus, $\sqrt{0.0004} = 0.02$.
In some cases, square roots of decimals may not result in a perfect square, meaning they may have an irrational square root. For instance, $\sqrt{0.5}$ will not give a whole number but an approximation:
We know that $\sqrt{0.5} \approx 0.7071$ (rounded to four decimal places).
It is important to use accurate methods or a calculator to find the square roots of decimals that do not have perfect square roots.
Another way to approach finding square roots of decimals is to use long division, just as one does for whole numbers. This method helps to find square roots to the required decimal places without relying on approximations.
In conclusion, the main idea of finding square roots of decimals involves shifting the decimal point to create a whole number, calculating the square root of the whole number, and then returning the decimal point to its proper place in the result.