Question

Find the square root of 100 and 196 by the method of repeated subtraction ?

Answer 1

10 and 14 will be root of 100 and 196

Answer 2

Answer:

The square root of 100 and 196 are 10 and 14 respectively.

Step-by-step explanation:

As explained in property of Square Numbers that square number is the sum of successive odd numbers starting from 1.

Therefore, you can find square root of a number by repeatedly subtracting successive odd numbers(starting from 1) from the given square number, till you get zero.

Finding square root of 100 by method of repeated subtraction:

This proceed as

$Step 1 : 100-1=99\\Step 2 : 99-3=96\\Step 3 : 96-5=91\\Step 4 : 91-7=84\\Step 5 : 8-9=75\\Step 6 : 75-11=64\\Step 7 : 64-13=51\\Step 8 : 51-15=36\\Step 9 :36-17=19\\Step 10 : 19-19=0$

Since we get 0 at the the tenth step of subtraction, therefore the square root of 100 is 10.

                                        ∴$\sqrt{100\\}$ = $100$

Finding square root of 196 by method of repeated subtraction:

This proceed as

$Step 1 :196-1=195\\Step 2:195-3=192\\Step 3:192-5=187\\Step 4:187-7=180\\Step 5:180-9=171\\Step 6:171-11=160\\Step 7 :160-13=147\\Step 8 : 147-15=132\\Step9:132-17=115\\Step 10:115-19=96\\Step 11:96-21=75\\Step 12:75-23=52\\Step13:52-25=27\\Step 14:27-27=0$

Since we get 0 at the the fourteenth step of subtraction, therefore the square root of 196 is 14.

                                     ∴$\sqrt{196} =14$