how to find or solve a cube root with whole number in a shortcut way .
Hey guys, I saw a faster way to find cube roots.
We already know some basic cube numbers
0^3=0
1^3=1
2^3=8
3^3=27
4^3=64
5^3=125
6^3=216
7^3=343
8^3=512
9^3=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.
how to find or solve a square root with a whole number in a shortcut way.
In Banking, Placement and Management Exams, the Quant section will often test your speed. You need to be quick with calculations if you want to ace the exam. You can use this shortcut to quickly find the square root of a number which is a perfect square! We can even find square root of large numbers. But this method is most ideally used for four or five digit perfect squares. You can use this trick for SSC CGL, SSC CPO, Railways Group D, RPF & ALP.
Unit Digits of Squares
First we need to remember unit digits of all squares from 1 to 10. The figure below shows the unit digits of the squares.
Now from the picture we can say that, whenever the unit digit of a number is 9, unit digit of the square root of that number will be definitely 3 or 7. Similarly, this can be applied to other numbers with different unit digits.
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Let’s learn how to find square root by taking different examples.
Example: Find the square root of 4489.
We group the last pair of digits, and the rest of the digits together.
Now, since the unit digit of 4489 is 9. So we can say that unit digit of its square root will be either 3 or 7.
Now consider first two digits i.e. 44. Since 44 comes in between the squares of 6 and 7 (i.e. 62 < 44 < 72), so we can definitely say that the ten’s digit of the square root of 4489 will be 6. So far, we can say that the square root will be either 63 or 67.
Now we will find the exact unit digit.
To find the exact unit digit, we consider the ten’s digit i.e. 6 and the next term i.e. 7.
Multiply these two terms
Since, 44 is greater than 42. So square root of 4489 will be the bigger of the two options i.e. 67.
Let us take another example.
Example: What is the square root of 7056?
Unit digit will be 4 or 6.
Since, 82 < 70 < 92
So the square root will be either 84 or 86.
Now consider 8 and 9
Since, 70 is less than 72. So square root will be the lesser of the two values i.e. 84.
Let’s try it out with five digit numbers now!
How to Find Square Root of a Five Digit Number
We pair the digits up starting from the right side. Since there is one extra left over after two pairs are formed, we club it with the pair closest to it.
Example: √(16641) = ?
Unit digit will be 1 or 9.
Since, 122 < 166 < 132
So, the square root will definitely be 121 or 129.
Now, consider 12 and 13
Since, 166 is greater the 156, we pick the larger of the options i.e. 129.
Let’s take another example, so that this trick will be clear to you.
Example: √(33489) = ?
Unit digit will be 3 or 7.
Since, 182 < 334 < 192
So, square root will be 183 or 187.
Now consider 18 and 19.
Now, 334 is less than 342. So, the square root will be lesser of the two numbers i.e. 183.
This trick to find square root of a number will surely help you in your exams. Now that you have learnt the basics, take different examples and practice some more.
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