SQUARE ROOT AND CUBE ROOT

!!! Before starting the chapter, I hope you will learn square of 1 to 25 and cube of 1 to 20 !!!

SQUARE ROOT:

First of all, we will see what comes as last digit after square of last digits of any number:

HINT 1: 1²=1, 2²=4, 3²=9, 4²=6, 5²=5, 6²=6, 7²=9, 8²=4, 9²=1

Here we can see square of any number cannot have last digit as 2,3,7,8. So, if any number consist these digits as last digit cannot be a perfect square.

Now, we have to determine square root of a number having ‘n’ digits.

:: If n is odd, then there are (n+1)/2 digits in its square root.

: : If n is even, then there are n/2 digits in its square root.

So, If n=1,2 then square root contains ‘1’ digit

If n=3,4 then square root contains ‘2’ digit

If n=5, then square root contains ‘3’ digit

For example- (1)square root of 729

It consist 3 digits so square root of 729 should have (3+1)/2=2 digits (_ _) in it.

And last digit should be 3 or 7 , as per HINT 1

Now for first digit determination, 729 is lies between 20²=400 & 30²=900, so first digit should be 2.

So, answer is 23 or 27. As 729 is close to 900 as compare to  400. Thus correct answer is “27”.

Example- (2)square root of 232324

It consist 6 digits so square root of 232324 should have 6/2=3 digits (_ _ _) in it.

And last digit should be 2 or 8 , as per HINT 1

Now for first two digits determination, 232324 is lies between 480²=230400 & 490²=240100, so first two digits should be 48.

So, answer is 482 or 488. As 232324 is close to 230400 as compare to  240100. Thus correct answer is “482”.

CUBE ROOT:

First of all, we will see what comes as last digit after square of last digits of any number:

HINT 2: 1³=1, 2³=8, 3³=7, 4³=4, 5³=5, 6³=6, 7³=3, 8³=2, 9³=9

Here we can see cube of any number can have last digit as 1-9.

Now, we have to determine cube root of a number having ‘n’ digits.

:: If n = 1,2,3 then cube root contains ‘1’ digit

:: If n = 4,5,6 then cube root contains ‘2’ digit

:: If n = 7,8,9 then cube root contains ‘3’ digit

For example- (1)cube root of 1331

It consist 4 digits so cube root of 1331 should have 2 digits (_ _) in it.

And last digit should be 1, as per HINT 2

Now for first digit determination, 1331 is lies between 10³=1000 & 20³=8000, so first digit should be 1.

Thus correct answer is “11”.

Example- (2)cube root of 1860867

It consist 7 digits so cube root of 1860867 should have 3 digits (_ _ _) in it.

And last digit should be 3, as per HINT 2

Now for first two digits determination, 186086731 is lies between 120³=1728000 & 130³=2197000, so first two digits should be 12.

Thus correct answer is “123”.

For more study material- visit my blog: studysyndrome.blogspot.in

And to read my poems- visit my blog : magicalemotion.blogspot.in