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Answered on 13 Jan Tuition

Harsh Agarwal

British wanted division of Bengal for efficient administration (according to them). In reality, they were following the policy of divide and rule by separating Hindu Muslim.
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Answered on 08/12/2020 Tuition

Ejaz Hassan

Teaching Accountancy and Economics for over 10 years. Overall teaching experience over 16 years.

Firstly you have to get registered for the CA foundation course on the official website of ICAI. They'll provide the syllabus and study material. You can proceed for self-study because most of the syllabus is from class XI and XII. Otherwise, you may also opt for online classes.
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Answered 5 days ago Tuition/Class I-V Tuition/French

Harsh Agarwal

If you are giving 2 hours per day, it will take a month to grasp the language.
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Answered on 07/11/2020 Tuition

Navneet Singh

Helping students reach their potential.

Fixation of atmospheric nitrogen by the microorganisms into the absorbable form, so that plants can take it up is called nitrogen fixation.
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Answered on 27/04/2019 Tuition CBSE/Class 9/Mathematics

Bhaskar

IIT-JEE LECTURER

Regular classes are always useful. Home tuitions are better than classroom coaching. Classroom coaching is better than online courses.Online classes are better when capable tutors are not available near to you. Advantage of online tuitions is we can select the best tutors around the globe (world)... read more

Regular classes are always useful. Home tuitions are better than classroom coaching. Classroom coaching is better than online courses.
Online classes are better when capable tutors are not available near to you. Advantage of online tuitions is we can select the best tutors around the globe (world).

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Answered on 23/03/2020 CBSE/Class 9/Social Studies Tuition/Class IX-X Tuition

Apoorva P.

The biggest waterfall in India is the Kunchikal waterfalls. It is located on the Shimoga - Udupi border of Karnataka. The water that flows down the waterfall is from the river Varahi. It is ranked as the 116th in the world and India highest waterfall. The waterfalls from a height of 455meters, in a cascading... read more

The biggest waterfall in India is the Kunchikal waterfalls. It is located on the Shimoga - Udupi border of Karnataka. The water that flows down the waterfall is from the river Varahi. It is ranked as the 116th in the world and India highest waterfall. The waterfalls from a height of 455meters, in a cascading manner over the rocky structures. The waterfalls close to the Hulikal Ghati Temple.

 

The water directly falls into the reservoir of the Mani dam, which greatly cuts down the speed of the flow of water. A hydraulic power plat is also built at the foot of the waterfalls, to generate electricity. 

 

The right time to visit this waterfall is during the rainy season. During this season, the waterfall is surrounded by greenery, and it is a delight to watch the tributaries formed by the Varahi river, as it falls into the waterfall.

 

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Answered on 09/12/2017 CBSE/Class 10/Science Tuition/Class IX-X Tuition

Vaibhav Kogje Vaibhav Kogje

Tutor

Resistance of each and every conducting material is different for example but its range starts from 10^-8 but the two most used metal are Lithium 9.28 10 8 and iron 9.71 10 8.
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Lesson Posted on 21/03/2017 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition

Fastest way How to check if a number is a Perfect Square or not

Debraj Paul

I had completed b.Tech,m.Tech (d). I am an experienced, qualified icse board school teacher with over...

Squares of all integers are known as perfect squares. In this lesson, we will discuss a very interesting Mathematical shortcut: How to check whether a number is a perfect square or not. There are some properties of perfect squares which can be used to test if a number is a perfect square or not. They... read more

Squares of all integers are known as perfect squares. In this lesson, we will discuss a very interesting Mathematical shortcut: How to check whether a number is a perfect square or not. There are some properties of perfect squares which can be used to test if a number is a perfect square or not. They can definitely say if it is not the square. (i.e. Converse is not necessarily true). 

All perfect squares end in 1, 4, 5, 6, 9 or 00 (i.e. Even number of zeros). Therefore, a number that ends in 2, 3, 7 or 8 is not a perfect square. 

For all the numbers ending in 1, 4, 5, 6, & 9 and for numbers ending in even zeros, then remove the zeros at the end of the number and apply following tests:

  • Digital roots are 1, 4, 7 or 9. No number can be a perfect square unless its digital root is 1, 4, 7, or 9. You might already be familiar with computing digital roots. (To find digital root of a number, add all its digits. If this sum is more than 9, add the digits of this sum. The single digit obtained at the end is the digital root of the number.)
  • If unit digit ends in 5, ten’s digit is always 2.
  • If it ends in 6, ten’s digit is always odd (1, 3, 5, 7, and 9) otherwise it is always even. That is if it ends in 1, 4, and 9 the ten’s digit is always even (2, 4, 6, 8, 0).
  • If a number is divisible by 4, its square leaves a remainder 0 when divided by 8.
  • Square of even number not divisible by 4 leaves remainder 4 while square of an odd number always leaves remainder 1 when divided by 8.
  • Total numbers of prime factors of a perfect square are always odd.

4539 ends in 9, digit sum is 3. Therefore, 4539 is not a perfect square.

5776 ends in 6, digit sum is 7. Therefore, 5776 may be a perfect square. 

Step 1: A perfect square never ends in 2, 3, 7 or 8. 

This is the first observation you will make to check if the number is a perfect square or not. For example, consider the example 15623. 

15623

By just noticing the number itself, we can conclude that 15623 cannot be a perfect square. We do not have to go to Step 2.


Step 2: Obtain the digital root of the number: 

How does the digital root of a number would help in determining if a number is a perfect square or not. It turns out; a perfect square will always have a digital root of 0, 1, 4 or 7. 

Take the number 15626 for example. This number ends in digits 6. So it satisfies Step 1. But still we cannot conclude, this number as a perfect square.

Let’s take the digital root of this number. 

1 5 6 2 6 = 5 + 6 = 11 = 1 + 1 = 2

So, the digital root of this number is 2. A perfect square will never have a digital root 2. Hence, we can conclude 15626 is not a perfect square.
Now, there is a rider for this shortcut though, even if both Steps are satisfied, that does not guarantee that the number is a perfect square. 

Let us take up an example here. Consider the number 623461, which is not a perfect square.
Notice that the unit digit is 1. This number could be a perfect square. Let us take the digital root. 

6 2 3 4 6 1

The digital root of 623461 is 4. So it satisfies both Step 1 and 2. Still we cannot conclude that 623461 is a perfect square though.
However, this shortcut comes in really handy to eliminate obvious choices which are not a perfect square to solve competitive examination where you need to find the perfect squares.


Is 14798678562 a perfect square? Is 15763530163289 a perfect square?

Examine both the units digits and the digital roots of perfect squares to help determine whether or not a given number is a perfect square.

As we know a perfect square can only end in a 0, 1, 4, 5, 6, or 9; this should allow us to determine whether the first of our numbers is a perfect square. However, it isn't sufficient to draw a conclusion about the second number. 

Again as we know that if a perfect square ends in 9; it’s tens digit is always even. Alas, even if we do this, it won't rule out numbers ending in 89, because '...89' is a possible square. 

However, as we know no number can be a perfect square unless its digital root is 1, 4, 7, or 9; so, find the digital root of our second number. It’s 5. As 5 isn't in this list, then the number is definitely not a perfect square. 

So, we can conclude, a number cannot be an exact or perfect square if:

-        it ends in 2, 3,7 or 8

-        it terminates in an odd number of zeros

-        its last digit is 6 but its penultimate (tens) digit is even

-        its last digit is not 6 but its penultimate (tens) digit is odd

-        its last digit is 5 but its penultimate (tens) digit is other than 2

-        its last 2 digits are not divisible by 4 if it is even numbe

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Answered on 24/02/2018 Tuition/Class VI-VIII Tuition

Sujoy D.

Tutor

90, 91, 92, 93, 94, 95, 96.
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Answered on 06/02/2019 Tuition/Class XI-XII Tuition (PUC)

Vishal

Charge
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