Find the square root of 441 by using
a) Repeated subtraction method
b) Prime factorization method
c) Division method
Answers
Answer:
Here are the Steps of Long Division Method for Finding Square Roots:
Step I: Group the digits in pairs, starting with the digit in the units place. Each pair and the remaining digit (if any) is called a period.
Step II: Think of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.
Step III: Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
Step IV: Now, the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend.
Step V: Repeat steps (2), (3) and (4) till all the periods have been taken up. Now, the quotient so obtained is the required square root of the given number.
That is answer ,using division method.
Prime Factorisation Method
Solving 441 into prime factors, we get :
441 = 1 × 1 × 21 × 21
441 = 1 × 21 × 1 × 21
Taking one number out from each pair of the prime number, we get
√441 = 1 × 21
.°. The square root will be = 1 × 21 = 21
This is by using prime factorization method.
441 - 1 = 440
440 - 3 = 437
437 - 5 = 432
432 - 7 = 425
435 - 9 = 426
426 - 11 = 415
415 - 13 = 402
402 - 15 = 387
387 - 17 = 370
370 - 19 = 351
351 - 21 = 330
330 - 23 = 307
307 - 25 = 282
282 - 27 = 255
255 - 29 = 226
226 - 31 = 195
195 - 33 = 162
162 - 35 = 127
127 - 37 = 90
80 - 39 = 41
41 - 41 = 0
it takes 21 steps to reach 0 by successive subtraction
Therefore , square root of 441 is 21
Hope this was useful
Step-by-step explanation:
Answer:
number 441
Step-by-step explanation:
repeated subtraction method =
441-1=440
440-3=437
437-5=432
432-7=425
425-9=416
416-11=405
405-13= 392
392-15= 377
377-17=360
360-19=341
341- 21=320
320-23=297
297-25=272
272- 27= 245
245-29=216
216-31=185
185-33=152
152-35=117
117-37=80
80-39=41
41-41=0
since we got 0 in 21 steps .
SO.the square root of 441= 21
''
''
prime factorization method
441 divided by 3 =147
147 divided by 3 = 49
49 divided by 7=7
7 divided by 7=1
441 = 3*3*7*7 = 3*7 = 21
,,
,,
the answer will be same in this method also.