Question

Find √x geomatrically, For x being any positive real number.​

Answer 1

Answer:

Yes I know this will a big explanatio but if you wrote on paper like this you will get full marks

Step-by-step explanation:

We now show how to find √x for any given positive real number 'x' geometrically.

For example, let us assume x = 4.5

We shall now find √4.5 geometrically.

PQ = 4.5 on a number line Mark the distance 4.5 units from a fixed point P on a given line to obtain a point Q such that PQ = 4.5 units.

From Q, mark a distance of 1 unit and mark the new point as R.

Find the mid-point of PR and mark that point as O.

Draw a semicircle with center O and radius OR.

Draw a line perpendicular to PR passing through Q and intersecting the semicircle at S.

Then, QS = √4.5

Square root of (4.5) More generally, to find √x, for any positive real number x:

Mark Q so that

PQ = x units

Mark R so that QR = 1 unit. Refer figure below.

Square root of x

Then, as we have done for the case x = 4.5, we have QS = √x

We can prove this result using the Pythagoras Theorem.

From figure, ΔOQS is a right angled triangle. Also, the radius of the circle is This shows that QS   = √x

This construction gives us a visual, and geometric way of showing that √x exists.

for all real numbers x > 0.

To represent √x on a number line:

If you want to know the position of √x on the number line,

then let us treat the line QR as the number line, with Q as zero, R as 1, and so on.

Draw an arc with center Q and radius QS, which intersects the number line in T.

Square root of x on a number line Thus, T represents √ x.