Question

on the number line represent root 7.3

Answer 1

Answer:

√7.3

Step-by-step explanation:

Draw a line AB = 7.3 units. Produce or extend the line at A by 1 unit, call this extended point C. Now AC=1, AB=7.3. Now, draw a perpendicular bisector of CB. Let the midpoint of CB be D.

Draw the circle with D as centre and DB or DC as radius. The radius of the circle is (1+7.3)/2 .

Now the distance AD = DC - AC = { (1+7.3)/2 - (1) } = (7.3–1)/2

From A draw a perpendicular to the line AB. Let this perpendicular touch the circle at P.

Now, PD = radius of the circle = (1+7.3)/2, AD is (7.3–1)/2 as determined above. Triangle APD is a right triangle with DP as hypotenuse and AD as one side. The other side AP is therefore,

AP² = DP²- AD² = [ { (1+7.3)/2 }² - { (7.3–1)/2 }² ] = (4x7.3)/4 = 7.3.

Therefore AP = sqrt (7.3).

This method can be used for constructing the square root of any number.