Let us understand representation of irrational number on number line. click on the Link to Watch the VIDEO explanation:Watch Video
Representation Of Irrational Numbers On The Number Line
Determine on the number line, the points which represent the irrational numbers root 3 and -root3.
Solution:
Mark points 0, 1, 2, -1, -2 on the number line l. Let A denote the point 0 and B denote the point 1 on the number line.
Draw a line perpendicular to AB at B and mark a point C on this perpendicular such that BC = 1 cm.
Join AC.
Let us calculate the value of AC. Appling the Pythagoras theorem to triangle ACB we have AC equal to AB square plus BC square i.e. equal to root of 1 square plus root of 1 square equal to root 2.
Now draw a perpendicular to AC at C and marking 90 degrees mark the point D on this perpendicular such that CD = 1 cm.
Join A to D
Applying Pythagoras theorem to triangle ACD we get Ad is equal to root of Ac square plus CD square.
Therefore, AD is equal to root 3
Now, with A as centre and AD as radius, draw an arc with a compass. This arc cuts the number line l at points P and Q. The point P represents root 3 on the positive half line and point Q represents - root 3 on the negative side of the number line.
Representation Of Irrational Numbers On The Number Line
Determine on the number line, the points which represent the irrational numbers root 3 and -root3.
Solution:
Mark points 0, 1, 2, -1, -2 on the number line l. Let A denote the point 0 and B denote the point 1 on the number line.
Draw a line perpendicular to AB at B and mark a point C on this perpendicular such that BC = 1 cm.
Join AC.
Let us calculate the value of AC. Appling the Pythagoras theorem to triangle ACB we have AC equal to AB square plus BC square i.e. equal to root of 1 square plus root of 1 square equal to root 2.
Now draw a perpendicular to AC at C and marking 90 degrees mark the point D on this perpendicular such that CD = 1 cm.
Join A to D
Applying Pythagoras theorem to triangle ACD we get Ad is equal to root of Ac square plus CD square.
Therefore, AD is equal to root 3
Now, with A as centre and AD as radius, draw an arc with a compass. This arc cuts the number line l at points P and Q. The point P represents root 3 on the positive half line and point Q represents - root 3 on the negative side of the number line.
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