In this page, square of a number and square root of a number are revised. The long division method to find the square root is explained.
We studied in exponents that .
An exponent of power is called square of the number.
eg: Square of is .
The word "square" means : the 2D shape of equal sides and angles" between the sides. The exponent square is representative of "area of the shape square, side to the power ".
We studied in the exponents that ".
An exponent of power or the nd root is called square root of the number.
eg: Square root of is .
The power of the root need not be mentioned for square roots
Square of is .
Square root of is .
the symbol is the square root.
Square of a number : A number multiplied by itself is the square of the number.
Square Root of a number : Square root of a value is the number whose square is the given value.
eg: as .
The factors of are ""
The factors of are ""
The prime factorization of is .
A procedure is illustrated in the figure.
finding square roots
Consider finding the result of .
Square root is a form of root. In roots, we learned to perform prime factorization to find the root.
Finding Square Roots : To find square root of a number, express the number in prime factors and group the factors.
Note: This method is suitable for finding square roots resulting in integers.
What is the
The answer is "".
Using the prime factorization method
The prime factorization method is suitable for square roots resulting in integer values.
Square root of a number can be given as
is a digit number with tens-units places
is a number that has at tens-units places
This understanding gives a method to eliminate and look at to choose the highest digit of the square root.
The rearranged one with gives the method to multiply by (which is ) and append a value , which is . Then multiply to .
In this process, the choice of and make the square root
The above process is explained for 2 digit square root and is easily extended for higher number of digits.
example using the procedure
The above steps is used in reverse when the square root is not known
This procedure is illustrated in the figure.
Procedure to finding Square Root of a number : Long division method is illustrated in the figure.
The outline of material to learn "Exponents" is as follows.
Note: click here for detailed outline of Exponents s
→ Representation of Exponents
→ Inverse of exponent : root
→ Inverse of exponent : Logarithm
→ Common and Natural Logarithms
→ Exponents Arithmetics
→ Logarithm Arithmetics
→ Numerical Expressions
→ PEMA / BOMA
→ Squares and Square roots
→ Cubes and Cube roots