The point 'R' shows the irrational number √11 on the given number line and for better proximation using decimals, 3.2×3.2= 10.24;3.4×3.4= 11.56
Step-by-step explanation:
It is given that we have to locate √11 on a number line, so for that we need to mark point 'O' on the number line as shown;
Now,
On the number line, point 'O' represent 0 and the point 'L' represents 3. Thus, we have OL = 3 units.
Now, we will construct LM = 1 unit, which will be perpendicular to the number line given;
=> OM = √10
Now, we will further construct MN = 1 unit, which will be perpendicular to OM;
=> ON² = OM² + MN²
=> ON = √OM² + MN²
=> √(10)² + (1)²
=> √10+1
=> √11
Furthermore, With O as the center and ON = √11 for the radius, we create an arc that crosses the number line at R resulting that line OR = √11 (radius).
Therefore, the point 'R' shows the irrational number √11 on the given number line.
For better proximation using decimals, the answers are:
3.2 × 3.2 = 10.24
3.4 × 3.4 = 11.56
<u>To know more about representation on number line, click here</u>:
