Question

Represent root 8 on the number line

Answer 1

Answer:

Following are the steps to represent $\sqrt 8$ on the number line:

1. A line is drawn of desired length.

2. A right angled triangle ∆ XYZ is constructed such that XY = 2units, and YZ = 2 units.

3. Hence, using Pythagoras Theorem,  

$\mathrm { XZ } = \sqrt { X Y ^ { 2 } + Y Z ^ { 2 } } = \sqrt { 2 ^ { 2 } + 2 ^ { 2 } } = \sqrt { 4 + 4 } = \sqrt { 8 }$

4. Taking X as the centre point and XZ as radius, an arc cutting the number line is drawn at A.

5. Hence the point A represents XZ = XA = $\sqrt 8$

Thus the point A represents $\sqrt 8$ on the number line.

The value of $\sqrt 8$ mathematically is,

$\sqrt 8 = \sqrt {4\times2} \\\\\sqrt 8=2\sqrt 2\\\\\sqrt 8 = 2\times1.414\\\\\sqrt 8 =2.828$