Question

Locate and plot √11 on a number line. Find a better approximation using decimals. 3.2×3.2= 3.4×3.4 = (Type integers or decimals.)​

Answer 1

Answer:

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

To know more about representation on number line, click here:

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