Construct a square of side 3 cm.

Step 1:
Draw a Ray AX. With A as center and radius 3cm cut an arc and name the intersecting point B.

Step 2:

With B as an center draw an arc intersecting the ray AX at P and Q.

Then with P as center and radius more than half of PQ cut an arc which intersects the previous arc at R and repeat the same for Q as center and name the intersecting point S.

Step 3:

Now with R as center draw an arc and then with S as center.

Name the intersecting point O.

Step 4:

Now B as center and 3cm as radius draw an arc that cuts the ray BO at C.

Step 5:

With C as center and radius 3cm draw an arc and repeat the same with A and name the intersecting point D.

Step 6:

Join AD and CD.

ABCD is required Square.