properties of square and square root class 8
Answers
Answer:
a perfect square cannot be negative and hence the square root of a negative number is not defined .
numbers ending with 1,4,5,6,9,will have a square root
if the unit digit of a number is2, 3 7,8, then a perfect square is not possible
Answer:
Perfect Squares
Perfect SquaresProperties of Square Numbers
Properties of square numbers are:
If a number has 0, 1, 4, 5, 6 or 9 in the unit’s place, then it may or may not be a square number. If a number has 2, 3, 7 or 8 in its units place then it is not a square number.
If a number has 1 or 9 in unit’s place, then it’s square ends in 1.
If a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.
Finding square of a number with unit’s place 5
The square of a number N5 is equal to (N(N+1))×100+25, where N can have one or more than one digit.
For example: 152=(1×2)×100+25=200+25=225
2052=(20×21)×100+25=42000+25=42025
Square Root
Square RootSquare Root of a Number
Finding the number whose square is known is known as finding the square root. Finding square root is inverse operation of finding the square of a number.
For example:
12=1, square root of 1 is 1.
22=4, square root of 4 is 2.
32=9, square root of 9 is 3.
Estimating the number of digits in the square root of a number
If a perfect square has n digits, then its square root will have n2 digits if n is even and (n+1)2 digits if n is odd.
For example: 100 has 3 digits, and its square root(10) has (3+1)2 =2 digits.
Estimating Square Roots
Estimating the Square Root
Estimating the square root of 247:
Since: 100 < 247 < 400
i.e. 10<√247<20
But it is not very close.
Also, 152=225<247 and 162=256>247
15<√247<16.
256 is much closer to 247 than 225.
Therefore, √247 is approximately equal to 16.
Introduction to Squares and Square Roots
Introduction to Squares and Square RootsIntroduction to Square Numbers
If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number.
Example: 1, 4, 9, 16 and 25.
Finding the Square of a Number
If n is a number, then its square is given as n×n=n2.
For example: Square of 5 is equal to 5×5=25
Finding square of a number using identity
Squares of numbers having two or more digits can easily be found by writing the number as the sum of two numbers.
For example:
232=(20+3)2 =20(20+3)+3(20+3)
=202+20×3+20×3+32
=400+60+60+9
=529
Step-by-step explanation:
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