Math, asked by 1234saru, 1 year ago

How to find square root and cube root with a trick

Answers

Answered by saitejassb
1
If a given number is at most 5-digited, it's quite easy to find its square root. Consider a number 11236. Here are the steps to find its square root.

Look at the unit digit of a number. It's 6 so the unit digit of its square root must be 4 or 6.

Now, try to find the range of its square root. 100^2 = 10,000 & 110^2 = 12,100. So, 100 < sqrt. < 110.So, the sqrt. should be 104 or 106.

You must be knowing the trick to find the square of a number with unit digit 5. If not, I tell you. 105^2 = (10*11) 25 = 11,025. As 11,236 > 11,025, the square root is 106.

If you are sure that a given number, here 11,236 is a perfect square, you need not verify it. But if you doubt, verify it by multiplying a square root, here 106 by itself.


Following the same procedure to find the square root of numbers having digits more than 5 is tedious & time consuming. But we hardly need to find their square rootsHey guys, I saw a faster way to find cube roots.

We already know some basic cube numbers

=0

=1

=8

=27

=64

=125

=216

=343

=512

=729

Now, the common thing here is that each ones digit of the cube numbers is the same number that is getting cubed , except for 2 ,8 ,3 ,7 .

now let us take a cube no like 226981 .

to see which is the cube root of that number , first check the last 3 digits that is 981 . Its last digit is 1 so therefore the last digit of the cube root of 226981 is 1 .

Now for the remaining digits that is 226

Now 226 is the nearer & bigger number compared to the cube of 6 (216)

So the cube root of 226981 is 61

Let us take another example - 148877

Here 7 is in the last digit but the cube of seven's last digit is not seven. But the cube of three has the last digit as 7.

So the last digit of the cube root of 148877 is 3.

Now for the remaining digits 148.

It is the nearer and bigger than the cube of 5 (125).

Therefore the cube root of 148877 is 53.

Let us take another example 54872.

Here the last three digit's (872) last digit is 2 but the cube of 2's last digit is not 2 but the last of the cube of 8 is 2.

So the last digit of the cube root of 54872 is 8.

Now of the remaining numbers (54). It is nearer and bigger to the cube of 3 (27). So therefore the cube root of 54872 is 38

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