Quadratic equation HOTS

If 3 cm & 5 cm are two sides of triangle whose area is 6 sq.cm. then find it's third side.

Angle bisector sum's solution

Angle bisector sum

Cube root by long division method

Method of cube root by long division method is similar to method of square root by long division method except:

1) in stead of adding the latest quotient part we have to add take full quotient

2) in stead of adding the number before multiplication we have to:

2a) find 300 x quotient square

2b) 30 x quotient

2c) take a judgement from step 2a) whiat will be next number

2d) multiply 2b) by that number

2e) take square of that number

2f) Add answers of 2a) 2 d) and 2e) and

2g) multiply 2f) by that number ( step 2c)'s judgement )

Any way the steps are re-written in order:

(1) Make groups of 3 digits starting from right-most (unit place digit) number.

(2) take the left-most group. It may have 1,2 or 3 numbers or digits

(3) find the largest cube less than this number.

(4) Subtract it from step (2)'s number. Write in quotient's place cube root of the number whose cube you have just now subtracted.

(5) Bring the next group of 3 numbers down i.e. write it besides the subtraction(remainder)  of the last step.

(6) Next number b you have to find such that [300 x a2 + 30a x b + b2] x b should be less than (as we have been doing in normal division method) (not much less than) this number.

Here "a"  is the quotient (answer of cube root) you have got till now.

(7a) Continue the procees by taking the steps (5) and (6) . If the given number is known to be a perfect cube or is a perfect cube, your process will stop when you come to last group of 3 digits.

In other words, continue the process till your last number lets you continue.

(7b) If the given number is not a perfect cube then you have to continue the process till you get 1 more place than the number of decimal points upto which you want accuracy.

Hope I have explained the method clearly. 2 3 1 1 2 Working for for Step 1 2 12 345 678 910 111 Working for Step 2 0 0 0 Step 1 8 1 1 1 4 345 a= 2 2 8 2 4345 b= 3 3 27 3 Step 2 4167 300a2 1200 3.620833 4 64 4 178 678 30a 60 30ax b 180 5 125 5 178678 b2 9 6 216 6 Step 3 159391 300a2+30ab+b2 Total 1389 7 343 7 19287 910 (300a2+30ab+b2) x b 4167 8 512 8 19287910 9 729 9 Step 4 16015231 3272679 111 Working for Step 3 Step 5 3272679111 23 3204709928 a= 23 67969183 b= 1 300a2 158700 1.125885 30a 690 30ax b 690 b2 1 300a2+30ab+b2 Total 159391 (300a2+30ab+b2) x b 159391 Working for Step 4 a= 231 b= 1 300a2 16008300 1.204869 30a 6930 30ax b 6930 b2 1 300a2+30ab+b2 Total 16015231 (300a2+30ab+b2) x b 16015231 Working for Step 5 a= 2311 b= 2 300a2 1602216300 2.042595 30a 69330 30ax b 138660 b2 4 300a2+30ab+b2 Total 1602354964 (300a2+30ab+b2) x b 3204709928 12345678910111 Cube root  23112.04241

Hemant's unique method

Quadratic Equations by Completing Square Method

Sums on Geometry chapter Circle

Squares of 1001 to 1031

Trick to remember squares of selected 4 digit numbers starting from 1000 till 1031.

Write "10", to its right double of last 2 digits from  given number say ex. 1024. Then 2x24=48.

to the right of this "1048" write square of 24 i.e. 576.
your answer is 1048576.