When a natural number is raised to the power 2 then it is called the square of the number. If a natural number is multiplied by itself, the result is a perfect square number which is also a natural number. Any natural number may not be a perfect square.
A square number can be expressed as the product of equal prime factors. A square number will always have either 0, 1, 4, 5 or 9 at the unit's place but the converse is not true.
Ex: 21 is not a square. If a natural number has either 2, 3, 7 or 8 at its unit place then it cannot be a square number. The square of an even number is always even while the square of an odd number is always odd. If two consecutive triangle numbers are added, we always obtain a square number. The sum of the first natural odd natural numbers is n 2. If a natural number is not the sum of consecutive odd natural numbers, starting from 1 then it cannot be a perfect square.
The square of any odd natural number greater than 1 is always the sum of two consecutive natural numbers. The square root of any number n is that number which when multiplied by itself gives the original number n.
The square root is the inverse function of finding square. Square roots are used to determine the length of the diagonal of a square or a triangle. When we need to calculate the third side of a triangle where the measurement of the other two sides of the triangle are known then square roots are used. Square roots are used to calculate the standard deviation. In order to solve a quadratic equation, square roots are used.
By Prime Factorization Method: To find the square root of a number by prime factorization method, first we need to derive the number and then determine the prime factors of the number by successive division. Then pair the derived prime factors in such a way that both the factors are equal in the pair. Calculate the product of one factor taken from each pair to obtain the desired square root. By Repeated Subtraction: This method is used when the natural numbers are small.
To calculate the number of odd numbers whose sum is the given natural number, we keep subtracting 1, 3, 5, 7, 9, �� till we arrive at 0. Then we count the number of times the subtraction is performed to arrive at 0.
The count becomes the square root of the number. Long Division Method: When the square numbers are big then we use the long division method because the prime factorization method becomes difficult. Then divide the leftmost digit of the given number by a number whose square root is less than or equal to the leftmost number of the given number.
Divide the number and write quotient and the remainder. Then pull the next paired digits next to the remainder and continue the division method till you arrive at 0. The derived quotient becomes the square root of the given number. This chapter is a very important chapter and also very lengthy but there is no need to feel scared, Vedantu has a team of very experienced teachers from reputed institutions across the country who can help you overcome your fears for the subject and master the topic.
There are a variety of sums given for the chapter in NCERT Solutions pdf which will give you an idea of what kind of question you can expect in exams. You can use the pdf of the solutions for your extensive practice for exams.
The solutions are designed by very experienced subject matter experts. They have designed the solutions in a very simple way by demonstrating in step wise so that it becomes self-explanatory. Vedantu has provided solutions to every question of the chapter and you can verify the answers with the solutions given. This will boost your confidence and will also help you with time management during the exams which is very important. This is the right platform for you to revise your subjects and score more marks in exams.
You can download on any device and practice as per your convenient time. You can carry the pdf anywhere and anytime.
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