How find the Square Root of a Perfect Square Number

[Snownam]

the last part lacks some reasoning for understanding

[vincentl]

You can actually calculate the square root of any number.
Separate the number into pairs of digits from the decimal point. 75 69.
Start with the first group 75, 8x8 = 64, 75-64 =11. Bring down the next pair of digits.
1169. You have 8- at the top, double that and put 16- at the left. 16- * -, use 7,
167 * 7 = 1169, 1169-1169=0, so finished.
You can continue beyond the decimal point to get as accurate as you desire.

[Allellen]

You lost me at start with 75 because why how do you know to do that? and how are you getting 8squared out of 75.

[NotaYoutuber]

You could also use divisibility rules to figure out the last digit. If you know 87 is divisible by 3, then you know 87^2 has to be divisible by 9. When you add the digits 7+5+6+9, you get 27, which is divisible by 9, meaning the square root has to be 87 and not 83.

Another example would be the square root of 4096. Is it 64 or 66? 66 is a multiple of 3, but 4+0+9+6 = 19, so it has to be 64. You could also check for divisibility by 8 in this case since 66 is only divisible by 2 once, which means 4 is the highest power of 2 that divides 66^2. This doesn’t work for every perfect square, but I thought I’d mention it.

[damianwrobel]

"8*(8+1)" comes from the FAST TRICK:
(x|5)^2 = (x*(x+1))|25

85^2 = (8|5)^2 = (8*(8+1))|25 = (8*9)|25 = 72|25 = 7225

7569 > 7225
7569 > 85^2
So
87^2 > 85^2

So the answer is 87.

Mr Hwang checked only first two digits of the number 7569 and only first two digits of the number 7225 (75>72) as it is enough to determinate if the solution is 83 or 87.


WARNING!
This FAST TRICK FAILS if given number is NOT a Perfect square, for example:
sqrt(7564) = ?
sqrt(7564) = 82 or 88

85^2 = (8*(8+1))|25 = 7225

7564 > 7225
So the answer should be 88, right?

NO!

Because 7564 is NOT a Perfect square...

To calculate sqrt(7564) you should use the "official" algorithm to calculate square of any number by hand.

Of course, sqrt(7564) = 88, ...
but
sqrt(7564) is NOT equal to 88.

So this FAST TRICK helps us to calculate only APPROXIMATE answer.

[ScholarXp]

Hello sir
And I from India because of you I was pass in my mathematics exam

[sajidrafique]

Mr H. I am 71 and I enjoy your videos for fun . You are amazing !

[aymantimjicht]

For example 64^2= 4096 the first digit is 6 for reason 36 is the smalist perfect sqt less then 40. To got a unite of 6 4*4 =16 then 64. thank you so match its Genius and Great.❤

[BigParadox]

Paradoxically It is even easier to find the cube root of perfect cubes, with a similar metod.

[rivenoak]

why was this not part of my lessons ? :(
it is so elegant

[daniellerosalie]

Thanks. This was something I did not know, and I minored in math.

[lynxb]

Take Squares of 80 and 90 i.e. 6400 & 8100 if no. is more close to 6400 then square root is 83 and if the no. is more close to 8100 then square root is 87. I chose 3 and 7 since only their squares give 9 as Unit digit

[Dibmis]

I have never seen such a ripped teacher in my life

[gspaulsson]

Just doing it in my head: it's >80 and <90. Must be odd and can't be 5, so 81, 83, 87 or 89. The units digit must be 9, so only 87 fits.

[maegansummers]

Thank you so much! This is the first square root video that actually makes sense!!

[usmanchughtai]

87. Got it under 10 seconds since the last digit 9 could only come from an 83 or 87

[debster]

Oh my goodness! Mr. Do you remember me from Torrance? It's Debby Gu - how are you doing?

[anestismoutafidis]

Σ{80^2=6400 + 30^2=900 +10^2=100+13^2=169}=7569
[30+10+13=53;=> 53^1/2=7, 28]
80+7=87 [87^2=7569] <=>
(7569)^1/2=87

[rockstaropgamer]

Find the squre of 1183 please immideatly

[marciomarquesdarocha]

Por mais que alguns alunos busquem caminhos rápidos, sempre haverá a necessidade de efetuar alguns cálculos. Eles precisam se convencer de que não existem caminhos que não exijam algum esforço.