Approximating Square Roots
The ‘square root’ of a given positive number ‘n’ is that number which, when multiplied by itself, gives ‘n’.
If the square root of a given number is not a whole number, then we can approximate the square root of a number.
Square Roots of Perfect Squares
Steps to approximate square roots:
Step 1: Think of two perfect squares between which the given number lies.
Example: If we want to find the square root of 12, then 32 = 9 and 42 = 16. So, lies between 9 and 16.
Step 2: Divide the given number by one of the two square roots in step 1.
12 ÷ 3 = 4
Step 3: Find the average of the root and the result in step 2.
Step 4: Repeat steps 2 and 3 until you reach the desired result.
Repetition of step 2: 12 ÷ 3.5 = 3.4285
Repetition of step 3: === 3.46425
Now you need to decide the level accuracy to find the square root of given number. If you want it to be more accurate, keep on repeating steps 2 and 3. We leave here.
Find the square root of the given numbers, rounded to the nearest tenth.
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