Math Problem Statement
Find the sq root of 10 by Division method.
Solution
To find the square root of 10 using the long division method, we follow a step-by-step process. This method is a traditional approach to calculating square roots manually, and it can be extended to find a decimal approximation of the square root of a non-perfect square like 10.
Steps:
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Pair the digits of the number starting from the decimal point:
- In this case, the number is 10. So we write it as (we can extend it with as many zeros as needed for the desired precision).
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Find the largest number whose square is less than or equal to the first pair:
- The first pair is 10. The largest integer whose square is less than or equal to 10 is 3 because . So, the quotient is 3, and the divisor is 3. Write 3 above the division line.
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Subtract the square of 3 from the first pair:
- . Bring down two zeros to make the number 100.
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Double the quotient for the new divisor:
- Double 3 to get 6. Now find a digit (let's call it X) such that is less than or equal to 100. The largest such X is 1 because .
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Subtract and bring down the next pair of zeros:
- . Bring down two more zeros, making it 3900.
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Update the divisor and repeat:
- Now, double the part of the quotient we have, which is 31, to get 62. We need to find the largest X such that is less than or equal to 3900. The largest such X is 6 because .
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Subtract and bring down the next pair of zeros:
- . Bring down two more zeros, making it 17400. Continue the process to get more decimal places.
After continuing this process, we find that:
Thus, the square root of 10, up to three decimal places, is approximately 3.162.
Would you like more details on any part of this process?
Related Questions:
- How do you find square roots for numbers larger than 100 using the division method?
- What is the square root of 5 using the division method?
- How does the division method compare with other methods of finding square roots, such as Newton’s method?
- Can the square root of a fraction (e.g., 1/2) be found using the long division method?
- How do we extend the division method for roots other than square roots, like cube roots?
Tip:
Practice the division method with smaller numbers first to become familiar with the process before moving on to larger or more complex numbers.
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Math Problem Analysis
Mathematical Concepts
Square Roots
Long Division Method
Decimal Approximation
Formulas
Square root calculation using long division
Theorems
Basic properties of square roots
Suitable Grade Level
Grades 8-10
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