Podcast
Questions and Answers
Which of the following is NOT a square number?
Which of the following is NOT a square number?
- 49
- 25
- 16
- 32 (correct)
If a natural number m can be expressed as $n^2$, where n is also a natural number, then m is a square number.
If a natural number m can be expressed as $n^2$, where n is also a natural number, then m is a square number.
True (A)
What are the possible ending digits (in the units place) for any square number?
What are the possible ending digits (in the units place) for any square number?
0, 1, 4, 5, 6, or 9
The numbers 1, 4, 9, 16... are called ________ squares because they can be expressed as the square of an integer.
The numbers 1, 4, 9, 16... are called ________ squares because they can be expressed as the square of an integer.
Match the number with their squares:
Match the number with their squares:
How many non-square numbers lie between $4^2$ and $5^2$?
How many non-square numbers lie between $4^2$ and $5^2$?
The square of an even number is always even, and the square of an odd number is always odd.
The square of an even number is always even, and the square of an odd number is always odd.
Express 49 as the sum of successive odd numbers starting from 1.
Express 49 as the sum of successive odd numbers starting from 1.
If a number has 'n' digits, then its square root will have n/2 digits if n is ________.
If a number has 'n' digits, then its square root will have n/2 digits if n is ________.
Match the square root with the correct number:
Match the square root with the correct number:
What is the unit digit of the square of 26387?
What is the unit digit of the square of 26387?
If a number ends in 2, 3, 7, or 8, it cannot be a perfect square.
If a number ends in 2, 3, 7, or 8, it cannot be a perfect square.
Find the value of $\sqrt{6400}$ using prime factorization.
Find the value of $\sqrt{6400}$ using prime factorization.
A group of three positive integers (a, b, c) is called a ________ triplet if $a^2 + b^2 = c^2$.
A group of three positive integers (a, b, c) is called a ________ triplet if $a^2 + b^2 = c^2$.
Match the following numbers with their prime factorizations:
Match the following numbers with their prime factorizations:
What is the smallest number by which 48 must be multiplied to obtain a perfect square?
What is the smallest number by which 48 must be multiplied to obtain a perfect square?
The square root of a perfect square always has an even number of digits.
The square root of a perfect square always has an even number of digits.
Write a Pythagorean triplet whose smallest member is 6.
Write a Pythagorean triplet whose smallest member is 6.
The inverse operation of squaring a number is finding its ________ _______.
The inverse operation of squaring a number is finding its ________ _______.
Match the Square root with its value:
Match the Square root with its value:
What is the value of (-9)²?
What is the value of (-9)²?
$\sqrt{4}$ = -2 is a correct statement.
$\sqrt{4}$ = -2 is a correct statement.
Find number of digits in the square root of 14400
Find number of digits in the square root of 14400
$\sqrt{81}$ = ________, and you can obtain result through repeatedly subtracting odd numbers starting from 1.
$\sqrt{81}$ = ________, and you can obtain result through repeatedly subtracting odd numbers starting from 1.
Match the square of a number with its prime factors:
Match the square of a number with its prime factors:
Flashcards
Square Numbers
Square Numbers
Numbers that can be expressed as the product of a number with itself (e.g., 1, 4, 9, 16, 25...).
Square Number (General)
Square Number (General)
Natural number 'm' that can be expressed as 'n²', where 'n' is also a natural number.
Ending Digits of Square Numbers
Ending Digits of Square Numbers
The digits in the units place will only be 0, 1, 4, 5, 6, or 9.
Adding Odd Numbers
Adding Odd Numbers
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Pythagorean Triplet
Pythagorean Triplet
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Generating Pythagorean Triplets
Generating Pythagorean Triplets
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Square Root
Square Root
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Finding Square Roots
Finding Square Roots
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Square Root by Repeated Subtraction
Square Root by Repeated Subtraction
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Square Root by Prime Factorization
Square Root by Prime Factorization
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Square Root by Division Method
Square Root by Division Method
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Study Notes
- The area of a square is side × side, where 'side' is the length of a side.
Square Numbers
- Numbers that can be expressed as the product of a number with itself are square numbers.
- Examples include 1, 4, 9, 16, and 25.
- If a natural number m can be expressed as n², where n is also a natural number, then m is a square number.
- 32 is not a square number because there is no natural number between 5 and 6 that, when squared, equals 32.
- Square numbers are also called perfect squares.
- The ending digits of square numbers are 0, 1, 4, 5, 6, or 9.
- If a square number ends in 6, the number whose square it is will have either 4 or 6 in the unit's place.
- Square numbers can only have an even number of zeros at the end.
Patterns
- Combining two consecutive triangular numbers results in a square number.
- For example, 1 + 3 = 4 = 2².
- Between the squares of numbers n and (n + 1), there are 2n non-perfect square numbers.
Adding Odd Numbers
- The sum of the first n odd natural numbers is n².
- If a number is a square number, it can be expressed as the sum of successive odd numbers starting from 1.
Expressing Odd Number Squares
- The square of any odd number can be expressed as the sum of two consecutive positive integers.
Product of Consecutive Even or Odd Natural Numbers
- (a + 1) × (a − 1) = a² – 1.
Finding the Square of a Number
- Numbers ending in 5 have a unique squaring pattern where (a5)² = a(a + 1) hundred + 25
Pythagorean Triplets
- A Pythagorean triplet is a set of three numbers a, b, and c, such that a² + b² = c².
- 2m, m² – 1, and m² + 1 forms a Pythagorean triplet for any natural number m > 1.
Finding Square Roots
- Finding the square root is the inverse operation of squaring.
- The positive square root of a number is denoted by the symbol √.
- Prime factorization can be used to find the square root of a number. Each prime factor in the square of a number occurs twice as often as in the number itself.
- To find the smallest multiple of a number that is a perfect square, identify unpaired prime factors in its prime factorization and multiply by those factors.
- Long Division Method to find the square root of large numbers.
- To find the square root of a decimal number, put bars on the integral part, starting from the unit's place, and on the decimal part, moving from the decimal point.
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