Square root by long division method

4299								18481401				99999999	OK	OK	OK	OK	OK	OK			Step1
												4	2	9	8	9	9	2			0	0	0		Step 3
Step 1		4										18	48	14	1	0	0	0			1	1	1		a=	42
	+	4									-	16									2	4	2		b=	9	10
Step 2		8	2									2	48								3	9	3		20a	840	10.01667
+	+		2										248								4	16	4		b=	9
Step 3			84	9	84	Tally						-	164								5	25	5		20a +b	849
		+		9									84	14							6	36	6		(20a+b)b	7641	OK
Step 4				858	8	858			Tally					8414							7	49	7
			+		8								-	7641							8	64	8		Step 4
Step 5					8596	9								773	1						9	81	9		a=	429
				+		9									77301							100			b=	8	9
Step 6						85978	9							-	68768						Step2				20a	8580	9.009441
					+		9								8533	0					a=	4			b=	8
Step 7							859798	2								853300					b=	2	3		20a +b	8596
								2							-	773802					20a	80	3.1		(20a+b)b	68768	OK
								8597984								79498	0				b=	2
								=2*square root									7949800				20a +b	82
								8597984								-	7738182				(20a+b)b	164	OK		Step 5
							= 2 x	4298992									211618	0							a=	4298
								0										21161800							b=	9	9
								Correct Answer									-	17195968							20a	85960	9.92671
																		3965832							b=	9
																									20a +b	85978
																		4299							(20a+b)b	773802	OK
																					Step 6				Step 7
																					a=	42989			a=	429899
																					b=	9	9		b=	2	2
																					20a	859780	9.246319		20a	8597980	2.461253
																					b=	9			b=	2
																					20a +b	859798			20a +b	8597984
																					(20a+b)b	7738182	OK		(20a+b)b	17195968	OK

compiled trick

Sum for 10 Standard SSC CBSE or ICSE based on Similarity H.O.T.S.

Circumcenter and Circumcircle of a triangle. My sum and new construction method

Length of angle bisector of right angle in right angled triangle

In triangle BCA, /_ C =90॰ BC=a CA=b.  Bisector of /_C meets BA at D. Find length of CD. (Hint: draw BF perpendicular on CD.)

1) Find area of the triangle BCA.

2) Find hypotenuse BA.

3)Find length of perpendicular CF on hypo. BA

4) Find BD and DA by angle bisector property / theorem.

5) Find area of triangle BCD.

6) Find BF = a sin 45॰

7) From area of triangle BCD find CD. using CD as base and BF as height.

(ab x sq root 2)/(a+b)

10 SSC 2020 onward pattern Q. 5 create your two own questions

Use 1+tan sq A= sec sq A to make question.
Two rational numbers are such that their difference and reciprocal of their sums is same and equal to k. Find the numbers.