Choose whether the given statement is true or false.is not on the real line.

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Accepted Answer

Step 1: we draw a number line as shown below where O is the center of the line and we write all positive integers on the right side and all negative integers on the left side.
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Step 2: Now, for representing

on the real number line, we make a right-angled triangle from the point O as shown below:
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Here, A is the point that denotes 1, the number line, so OA=1. Now we will draw a perpendicular from point A to point B , so that AB = 1because it is the same distance in the number as OA = 1.
Step 3: Now, by joining the points B and C,we get a right-angled triangle as shown below:
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By using Pythagoras theorem in the triangle OAB:

By substituting the values of OA = 1 and AB = 1 in the above expression

,we get:

By opening the brackets and adding inside the root, we get:

Step 4: Now, by again drawing a perpendicular from a point B to E of length 1 unit as shown below:
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By applying Pythagoras theorem in the right-angled triangle OEB with

and BE = 1 we get:

By substituting the values of

and BE=1 in the above expression

, we get:

By opening the brackets inside the root, we get:

By doing the addition of the brackets inside the root, we get:

Step 5: Now, we will draw an arc from the center point O by taking the radius OE which will cuts the number line into the right side of the center at the point M which will represent

the number line.
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The point

on the number line is
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Since, It is false.
The correct statement is: “

is on the real line. ”

Choose whether the given statement is true or false.
is not on the real line.

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