Tag: Squaring and Square Roots

Shortcuts for Squaring and Square Roots

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Speed Math Squaring 3-digit Number Squaring and Square Roots

[Speed Math] SQUARING 3-DIGIT NUMBER

Here’s an example of a SPEED MATH shortcut for SQUARING 3-DIGIT NUMBER : (Sq) 3D from the SQUARING AND SQUARE ROOTS category.

Squaring 3-digit Number

When can I use this method?

For squaring any 3 digit number.

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pdf Download Practice sheet for SQUARING 3-DIGIT NUMBER

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Notes –

  1. Notice the way the individual values are added.
  2. This method uses the concept of (a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac


Related Shortcuts –

Squaring 2-digit Number: (Sq) 2D


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Speed Math Squaring and Square Roots Squaring using Equidistant Method

[Speed Math] SQUARING USING EQUIDISTANT METHOD

Here’s an example of a SPEED MATH shortcut for SQUARING USING EQUIDISTANT METHOD : (Sq) Equidx from the SQUARING AND SQUARE ROOTS category.

Squaring using Equidistant Method

When can I use this method?

For squaring any 2-digit or 3-digit numbers.

One can also use this method to solve higher digit numbers as long as squaring of its component numbers is easy enough.

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pdf Download Practice sheet for SQUARING USING EQUIDISTANT METHOD

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Notes –

  1. This method uses the concept of a2 = [(a + b) (a – b)] + b2 = [a2 – b2] + b2
  2. Use the shortcut 2D or any other 2-digit squaring shortcut to square 2-digit components when squaring 3-digit numbers.

Related Shortcuts –

None


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Categories
Speed Math Squaring 3-digit Numbers near a Base Squaring and Square Roots

[Speed Math] SQUARING 3-DIGIT NUMBERS NEAR A BASE

Here’s an example of a SPEED MATH shortcut for SQUARING 3-DIGIT NUMBERS NEAR A BASE : (Sq) NrB2 from the SQUARING AND SQUARE ROOTS category.

Squaring 3-digit Numbers near a Base

 

When can I use this method?

For squaring any 3-digit numbers.

The number can be either < or > a Base number.

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pdf Download Practice sheet for SQUARING 3-DIGIT NUMBERS NEAR A BASE

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Notes –

  1. When selecting a Base number, prefer a number that is near the number to be squared as well as it should be easy to multiply with (prefer round numbers).
  2. This method uses the concept (B + a)2 = [(B + a) + a] + a2, where ‘(B + a)’ is the number to be squared, ‘B’ is the Base number and ‘a’ is the difference.
  3. Whenever the number is more than the Base number, the difference is written as positive (+ve).
  4. Whenever the number is less than Base Number, the difference is written as negative (-ve).
  5. This method is a corollary to the Multiplication method NrB3

Related Shortcuts –

Squaring Numbers near 100 : (Sq) Nr100

Squaring Numbers near 1000 : (Sq) Nr1000

Squaring Numbers near 50 : (Sq) Nr50

Squaring Numbers near 500 : (Sq) Nr500

Squaring 2-digit Numbers near a Base : (Sq) NrB2


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Categories
Speed Math Squaring 2-digit Numbers near a Base Squaring and Square Roots

[Speed Math] SQUARING 2-DIGIT NUMBERS NEAR A BASE

Here’s an example of a SPEED MATH shortcut for SQUARING 2-DIGIT NUMBERS NEAR A BASE : (Sq) NrB2 from the SQUARING AND SQUARE ROOTS category.

Squaring 2-digit Numbers near a Base

When can I use this method?

For squaring any 2-digit numbers.

The number can be either < or > a Base number.

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pdf Download Practice sheet for SQUARING 2-DIGIT NUMBERS NEAR A BASE

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Notes –

  1. When selecting a Base number, prefer a number that is near the number to be squared as well as it should be easy to multiply with (prefer round numbers).
  2. This method uses the concept (B + a)2 = [(B + a) + a] + a2, where ‘(B + a)’ is the number to be squared, ‘B’ is the Base number and ‘a’ is the difference.
  3. Whenever the number is more than the Base number, the difference is written as positive (+ve).
  4. Whenever the number is less than Base Number, the difference is written as negative (-ve).
  5. This method is a corollary to the Multiplication method NrB2

Related Shortcuts –

Squaring Numbers near 100 : (Sq) Nr100

Squaring Numbers near 1000 : (Sq) Nr1000

Squaring Numbers near 50 : (Sq) Nr50

Squaring Numbers near 500 : (Sq) Nr500

Squaring 3-digit Numbers near a Base : (Sq) NrB3


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Categories
Speed Math Squaring and Square Roots Squaring using Duplex Method

[Speed Math] SQUARING ANY NUMBER USING DUPLEX METHOD

Here’s an example of a SPEED MATH shortcut for SQUARING ANY NUMBER USING DUPLEX METHOD from the SQUARING AND SQUARE ROOTS category.

Make sure to check out DUPLEX CONCEPT to understand how Duplex values of numbers are calculated.

Squaring using Duplex Method

When can I use this method?

For squaring any number.

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pdf Download Practice sheet for SQUARING ANY NUMBER USING DUPLEX METHOD

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Notes –

  1. Make sure to check out DUPLEX CONCEPT to understand how Duplex values of numbers are calculated.
  2. Notice the patterns in which the digits are selected.
  3. Notice the way the individual values are added.
  4. This method uses the concept of (a + b +c +…)2 = a2 + b2 + c2 + … 2ab + 2bc + 2ac + … (It is a simplified version of the Multinomial Theorem)

Related Shortcuts –

None


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Categories
Speed Math Squaring and Square Roots Squaring Numbers near 500

[Speed Math] SQUARING NUMBERS NEAR 500

Here’s an example of a SPEED MATH shortcut for SQUARING NUMBERS NEAR 500 : (Sq) Nr500 from the SQUARING AND SQUARE ROOTS category.

Squaring Numbers near 500

When can I use this method?

For squaring numbers near 500.

The number can be either < or > 500.

One can use this method to square numbers away from 500 as long as it is comfortable to square the difference portions.

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pdf Download Practice sheet for SQUARING NUMBERS NEAR 500

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Notes –

  1. This method uses the concept (500 + a)2 = [(250 + a) 100] + a2, where ‘(500 + a)’ is the number near 500 and ‘a’ is difference.
  2. Whenever the number is more than 500, the difference is written as positive (+ve).
  3. Whenever the number is less than 500, the difference is written as negative (-ve).

Related Shortcuts –

Squaring Numbers near 100 : (Sq) Nr100

Squaring Numbers near 1000 : (Sq) Nr1000

Squaring Numbers near 50 : (Sq) Nr50

Squaring 2-digit Numbers near a Base : (Sq) NrB2

Squaring 3-digit Numbers near a Base : (Sq) NrB3


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Categories
Speed Math Squaring and Square Roots Squaring Numbers near 50

[Speed Math] SQUARING NUMBERS NEAR 50

Here’s an example of a SPEED MATH shortcut for SQUARING NUMBERS NEAR 50 : (Sq) Nr50 from the SQUARING AND SQUARE ROOTS category.

Squaring Numbers near 50

When can I use this method?

For squaring numbers near 50.

The number can be either < or > 50.

One can use this method to square numbers away from 50 as long as it is comfortable to square the difference portions.

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pdf Download Practice sheet for SQUARING NUMBERS NEAR 50

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Notes –

  1. This method uses the concept (50 + a)2 = [(25 + a) 100] + a2, where ‘(50 + a)’ is the number near 50 and ‘a’ is difference.
  2. Whenever the number is more than 50, the difference is written as positive (+ve).
  3. Whenever the number is less than 50, the difference is written as negative (-ve).

Related Shortcuts –

Squaring Numbers near 100 : (Sq) Nr100

Squaring Numbers near 1000 : (Sq) Nr1000

Squaring Numbers near 500 : (Sq) Nr500

Squaring 2-digit Numbers near a Base : (Sq) NrB2

Squaring 3-digit Numbers near a Base : (Sq) NrB3


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Categories
Speed Math Squaring and Square Roots Squaring Numbers near 1000

[Speed Math] SQUARING NUMBERS NEAR 1000

Here’s an example of a SPEED MATH shortcut for SQUARING NUMBERS NEAR 1000 : (Sq) Nr1000 from the SQUARING AND SQUARE ROOTS category.

Squaring Numbers near 1000

When can I use this method?

For squaring numbers near 1000.

The number can be either < or > 1000.

One can use this method to square numbers away from 1000 as long as it is comfortable to square the difference portions.

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pdf Download Practice sheet for SQUARING NUMBERS NEAR 1000

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Notes –

  1. This method uses the concept (1000 + a)2 = [(1000 + a) + a] + a2, where ‘(1000 + a)’ is the number near 1000 and ‘a’ is the difference.
  2. Whenever the number is more than 1000, the difference is written as positive (+ve).
  3. Whenever the number is less than 1000, the difference is written as negative (-ve).
  4. This method is a corollary to the Multiplication method Nr1000

Related Shortcuts –

Squaring Numbers near 100 : (Sq) Nr100

Squaring Numbers near 50 : (Sq) Nr50

Squaring Numbers near 500 : (Sq) Nr500

Squaring 2-digit Numbers near a Base : (Sq) NrB2

Squaring 3-digit Numbers near a Base : (Sq) NrB3


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Categories
Speed Math Squaring and Square Roots Squaring Numbers near 100

[Speed Math] SQUARING NUMBERS NEAR 100

Here’s an example of a SPEED MATH shortcut for SQUARING NUMBERS NEAR 100 : (Sq) Nr100 from the SQUARING AND SQUARE ROOTS category.

Squaring Numbers near 100

When can I use this method?

For squaring numbers near 100.

The number can be either < or > 100.

One can use this method to square numbers away from 100 as long as it is comfortable to square the difference portions.

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pdf Download Practice sheet for SQUARING NUMBERS NEAR 100

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Notes –

  1. This method uses the concept (100 + a)2 = [(100 + a) + a] + a2, where ‘(100 + a)’ is the number near 100 and ‘a’ is the difference.
  2. Whenever the number is more than 100, the difference is written as positive (+ve).
  3. Whenever the number is less than 100, the difference is written as negative (-ve).
  4. This method is a corollary to the Multiplication method Nr100

Related Shortcuts –

Squaring Numbers near 1000 : (Sq) Nr1000

Squaring Numbers near 50 : (Sq) Nr50

Squaring Numbers near 500 : (Sq) Nr500

Squaring 3-digit Numbers near a Base : (Sq) NrB3


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Categories
Speed Math Squaring and Square Roots Squaring Numbers ending with 5

[Speed Math] SQUARING NUMBERS ENDING WITH 5

Here’s an example of a SPEED MATH shortcut for SQUARING NUMBERS ENDING WITH 5 : (Sq) LD5dx from the SQUARING AND SQUARE ROOTS category.

Squaring Numbers ending with 5

When can I use this method?

For squaring 2-digit numbers or 3-digit numbers ending with 5.

One can also use this method to solve higher digit numbers as long as multiplication of numbers is easy enough.

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pdf Download Practice sheet for SQUARING NUMBERS ENDING WITH 5

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Notes –

  1. This method uses the concept (a + 5)2 = [a (a + 10)] + 25, where ‘(a + 5)’ is the number ending with 5 and ‘a’ is the tens place value of that number.

Related Shortcuts –

None

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