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how to find √x for any given positive real number x write steps of activity and represent it on a number line.
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how to find √x for any given positive real number x write steps of act...
For representation of real numbers on number line, use the following steps :
Represent √x on number line.
Step 1 Draw a line and mark a point A on it.
Step 2 Mark a point B on the line drawn such that AB = x cm.
Step 3 Mark a point C on AB produced such that BC = 1 cm.
Step 4 Find mid-point of AC (x+1). Let the mid-point be O.
Step 5 Taking O as centre and OC = OA [(x+1)/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at D
Step 6 Taking B as the centre and BD as radius draw an arc cutting OC produced at E.
Point E so obtained represents √x.
Represent √x on number line.
Step 1 Draw a line and mark a point A on it.
Step 2 Mark a point B on the line drawn such that AB = x cm.
Step 3 Mark a point C on AB produced such that BC = 1 cm.
Step 4 Find mid-point of AC (x+1). Let the mid-point be O.
Step 5 Taking O as centre and OC = OA [(x+1)/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at D
Step 6 Taking B as the centre and BD as radius draw an arc cutting OC produced at E.
Point E so obtained represents √x.
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how to find √x for any given positive real number x write steps of act...
Introduction:
Finding the square root of a given positive real number is a mathematical operation that involves calculating a number which, when multiplied by itself, results in the given number. The symbol used to represent the square root is √. In this guide, we will explain the steps involved in finding the square root of any positive real number x.
Steps to find the square root of a positive real number:
1. Start by estimating the square root of x to the nearest whole number.
2. Divide x by the estimated square root.
3. Average the result of the division with the estimated square root.
4. Repeat steps 2 and 3 until you reach a level of accuracy that you are satisfied with.
Example:
Let's take an example to understand the steps involved in finding the square root of a positive real number. Suppose we want to find the square root of 16.
1. Estimation: The nearest whole number to 16 is 4. Hence, we estimate the square root of 16 to be 4.
2. Division: Divide 16 by 4. The result is 4.
3. Averaging: Average 4 with the result of the division (4). The average is (4+4)/2 = 4.
4. Repeat: Repeat steps 2 and 3 until you reach a satisfactory level of accuracy.
The next iteration would be:
Division: Divide 16 by 4 = 4.
Averaging: Average 4 with 4 = 4.
As we can see, the result has not changed. Hence, we can conclude that the square root of 16 is 4.
Representation on a number line:
To represent the square root of a positive real number on a number line, we can plot the given number and its square root on the same line. For example, to represent the square root of 16 on a number line, we can plot 16 and 4 on the same line.
Conclusion:
Finding the square root of a positive real number involves a simple iterative process of estimation, division, and averaging. By following these steps, we can find the square root of any positive real number. Representing the square root of a positive real number on a number line is also a simple process of plotting the given number and its square root on the same line.
Finding the square root of a given positive real number is a mathematical operation that involves calculating a number which, when multiplied by itself, results in the given number. The symbol used to represent the square root is √. In this guide, we will explain the steps involved in finding the square root of any positive real number x.
Steps to find the square root of a positive real number:
1. Start by estimating the square root of x to the nearest whole number.
2. Divide x by the estimated square root.
3. Average the result of the division with the estimated square root.
4. Repeat steps 2 and 3 until you reach a level of accuracy that you are satisfied with.
Example:
Let's take an example to understand the steps involved in finding the square root of a positive real number. Suppose we want to find the square root of 16.
1. Estimation: The nearest whole number to 16 is 4. Hence, we estimate the square root of 16 to be 4.
2. Division: Divide 16 by 4. The result is 4.
3. Averaging: Average 4 with the result of the division (4). The average is (4+4)/2 = 4.
4. Repeat: Repeat steps 2 and 3 until you reach a satisfactory level of accuracy.
The next iteration would be:
Division: Divide 16 by 4 = 4.
Averaging: Average 4 with 4 = 4.
As we can see, the result has not changed. Hence, we can conclude that the square root of 16 is 4.
Representation on a number line:
To represent the square root of a positive real number on a number line, we can plot the given number and its square root on the same line. For example, to represent the square root of 16 on a number line, we can plot 16 and 4 on the same line.
Conclusion:
Finding the square root of a positive real number involves a simple iterative process of estimation, division, and averaging. By following these steps, we can find the square root of any positive real number. Representing the square root of a positive real number on a number line is also a simple process of plotting the given number and its square root on the same line.
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how to find √x for any given positive real number x write steps of activity and represent it on a number line. for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about how to find √x for any given positive real number x write steps of activity and represent it on a number line. covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how to find √x for any given positive real number x write steps of activity and represent it on a number line..
how to find √x for any given positive real number x write steps of activity and represent it on a number line. for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about how to find √x for any given positive real number x write steps of activity and represent it on a number line. covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how to find √x for any given positive real number x write steps of activity and represent it on a number line..
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