Pawan Prajapati
Last Activity: 3 Years ago
Hint: We know that 16−−√=4 and 17−−√=42+12−−−−−−√. Squaring both sides of the expression and constructing it on a number line. Follow the steps to represent the number on a number line and get the required figure.
Complete step by step answer:
The number system represents the numbers on a number line. Number system is a very useful and important concept in mathematics to represent the numbers on a number line. All types of numbers like natural numbers, whole numbers, rational numbers, Integers are represented on a number line. All the numbers natural numbers, whole numbers, rational numbers, integers are collectively called as real numbers
A number line is a line that serves as an abstraction of real numbers. Every point on a number line is assumed as a real number. The numbers on a number line are placed at equal intervals. According to the question it is given that the number is 17−−√.
Here,
17−−√can be written as,
⇒17−−√=42+12−−−−−−√
⇒17−−√=16+1−−−−−√
Squaring on both sides,
⇒(17−−√)2=42+12
Now, Construct 17−−√ on a number line,
Step 1: Draw a number line with equal marks on either side.
Step 2; Consider a point O at zero.
Step 3: Mark a point A at 4 such that OA is 4.
Step 4: Construct AB of unit length.
Step 4: Join AB
Step 5: Take OB as radius and intersect the number line at C.
Step 6: Finally, C represents 17−−√
Note:
Follow the steps carefully. If you miss any step in constructing the number on a number line, then you will get a wrong answer. A number line can extend infinitely in any direction. The left side of the number line is called the negative side and the right side is called the positive side.