Most students are uncomfortable with Math.
Most students would bunk the Maths period, if they could, wouldn’t they?
But why is that so?
Do they dislike or fear the subject
But Why.
Maths if taught well is a very interesting subject.
Moreover, academically, too it is an important subject.
When students go for higher education, a sound knowledge if Maths will give them the edge in choosing a discipline of their choice.
Maths is a universally important subject. 8th standard maths notes allow students to get some extra questions for revision and prepare well for exams. Parents and teachers can help dispel the doubts about Maths.
Allow students to explore the subject. Let them develop a good understanding of the basics. Moreover, take into account that every student will learn at a different pace.
This will help them to like the subject. Removing the pressure of focusing only on grades will help them in the long run.
Therefore, we have prepared this easy guide. This will help students gain a very basic understanding of the topic on decimals and finding the square root of a decimal number. Once the foundation is strong, then they can progress to solving the exercise in the NCERT book.
Let’s understand what are Decimals?
By now, 8th standard students are familiar with the term decimal.
Anyway, we will do a quick recap.
When we insert a point to separate two parts of a number, that point is termed as a decimal.
The number on the left hand side of the decimal is the whole number. Conversely, the number on the right hand side of the decimal point is a part of the whole number. However it has a value less than one.
Let us understand better with the help of numbers.
For instance 25.6
Here 25 is the whole number
It is followed by the point or the decimal and 0.6 is the decimal number. It has a values less than one.
Decimals are placed according to place values.
Basically, decimals are separators.
They separate the whole numbers from their lesser values, which have not yet reached a whole number value.
Using Examples to Explain Decimals
Students will understand better if we explain with the help of an example
For instance, you have a chocolate bar.
Numerically, you can write it as 1, 1.0 or 1/1.
However, what if you wanted to share it with five of your friends?
What will you do?
Obviously, you will divide it into five pieces.
Hence, you break up one whole into five smaller pieces of the whole.
So you will have 5 pieces which together represent the whole 1 piece
Numerically, you can denote each part as 1/5, 2/5, 3/5, 4/5 and 5/5 or 0.2, 0.4, 0.6, 0.8 and 1.
Basically, this means
One-fifth, two-fifths, three-fifths, four-fifths, and five-fifths.
Hope the quick revision on decimals is helpful!
Moving onto Squaring and Square Roots
Squaring- Lets understand the term
We will use numbers to explain the term .
For instance, we take the number 4
Now we need to carry out an operation
That is we need to multiply 4 with itself to square it.
Therefore, we carry out the operation
Hence multiplying 4 by itself gives me 16.
That is 4 x 4 = 16.
We have multiplied 4 two times. So we say 4 to the power 2.
Hence 4 squared is 16.
Do you want to understand with the help of another example?
Here goes
Let’s take 5 as a number
Similarly, we square 5 that is we multiply it twice with itself
Therefore 5 x 5 = 25.
Hence 5 squared is 25
Let’s move on to Square Roots
Conversely, to find the square root of a number we go backwards to find the squares. That is we need to understand which number when squared gives us the number we have.
For example lets take 9
So , we need to find which two numbers when multiplied by itself will give us 9
So is it 1×1- No
Or 2x 2 – Again no
What about 3×3- Yes as that gives me the result 9.
Hence 3 is the square root of 9.
Wasn’t that easy?
To demonstrate again with another example.
Find the square root of 36.
We know that 6 x 6 = 36.
Hence the square root of 36 is 6.
Related post: Top 12 Ways To Make Math Fun For Elementary Kids
Cube Roots
Just as we find the square root by multiplying twice, we find the cube root by multiplying thrice.
For instance 3 x 3 x 3= 27.
Hence the cube root of 27 is 3.
To summarise, square occurs when a number is multiplied by itself twice and cube when it is multiplied by itself three times.
Finding the Square Root of a Decimal Number
We will again proceed in the same way.
We will explain with the help of a live example using numbers.
If we only explain the theory, students might find it difficult to understand.
However, explaining with numbers will make it easier for them to understand.
We will use numbers to understand better. To find the square root of a decimal number, we will start with grouping or pairing of numbers
For instance, we take the number 761.76
We will show you in simple steps to find the square root for this number.
Firstly, start pairing the numbers.
Since there is a decimal point in between the numbers, we will apply pairing in opposite directions.
For the numbers on the left of the decimal, we will start paring from Left to right.
For numbers to the right of the decimal, we will start from right to left.
Hence we will have 7-61-.76.
Using the Long Division Method
We shall use this method. It is easy to understand.
Lets start with the solution.
Our number is 761.76. We have paired the numbers and shall start the division operation on it.
Firstly, we start with finding the number whose square is smaller than seven.
Obviously that number is 2. Why?
Because 2x 2= 4
It can’t be 3 since 3 x 3 = 9 which is bigger than 7
So we will divide 7 61. 76 by 2 first
So we get 7 – 4 which gives us 3
As illustrated, we bring 61 down and thereafter add the quotient to the divisor
What is our next step, now?
Well we find the number that can be combined with 4 and that combination number should be multiplied by the same number to give us a number equal to or less than 361
Hence the number is 7
Therefore we have 47 x 7 = 329
Hence our calculation now looks like
Now we bring down the next pair that is 76
Since 76 is after the decimal, we add a decimal in the quotient after 27.
To illustrate
Now we will add 7 in the divisor and leave a place for the next digit in the divisor.
Similarly, we again look for a number that when combined with 54 and multiplied by it should give a number equal to or less than 3276
Let’s take 6 and multiply 546 with 6
Hence we get the result 3276.
Now we insert 6 in the quotient bar after the decimal point. And now the remainder is zero.
Therefore the square root of 761.76 is 27.6
Hence solved.
Wrapping Up
To conclude, once students grasp the basic concepts, they can solve the problems.
Since square roots are an important chapter for grade 8 students, they should study the 8th standard maths notes thoroughly.
