square root

How to Square A Number

To square a number, just multiply it by itself ...

Example: What is 3 squared?

3 Squared

=

= 3 × 3 = 9

"Squared" is often written as a little 2 like this:

This says "4 Squared equals 16"
(the little 2 says the number appears twice in multiplying)

Squares From 0² to 6²

0 Squared	=	02	=	0 × 0	=	0
1 Squared	=	12	=	1 × 1	=	1
2 Squared	=	22	=	2 × 2	=	4
3 Squared	=	32	=	3 × 3	=	9
4 Squared	=	42	=	4 × 4	=	16
5 Squared	=	52	=	5 × 5	=	25
6 Squared	=	62	=	6 × 6	=	36

The squares are also on the Multiplication Table:

Negative Numbers

We can also square negative numbers.

Example: What happens when we square (−5) ?

Answer:

(−5) × (−5) = 25

(because a negative times a negative gives a positive)

That was interesting!

When we square a negative number we get a positive result.

Just the same as squaring a positive number:

(For more detail read Squares and Square Roots in Algebra)

Square Roots

A square root goes the other way:

3 squared is 9, so a square root of 9 is 3

A square root of a number is ...

... a value that can be multiplied by itself to give the original number.

A square root of 9 is ...

... 3, because when 3 is multiplied by itself we get 9.

How to find mean,median,mode

How to find the mean mode and median : Steps

How to find the mean mode and median:MODE

Step 1: Put the numbers in order so that you can clearly see patterns.
For example, lets say we have 2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99. The mode is the number that appears the most often. In this case: 44, which appears three times.

How to find the mean mode and median: MEAN

Step 2: Add the numbers up to get a total.
Example: 2 +19 + 44 + 44 +44 + 51 + 56 + 78 + 86 + 99 + 99 = 622.  Set this number aside for a moment.

Step 3: Count the amount of numbers in the series.
In our example (2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99), we have 11 numbers.

Step 4: Divide the number you found in step 2 by the number you found in step 3.
In our example: 622 / 11 = 56.5454545. This is the mean, sometimes called the average.

Dividing the sum by the number of items to find the mean.

How to find the mean mode and median: MEDIAN

If you had an odd number in step 3, go to step 5. If you had an even number, go to step 6.

Step 5: Find the number in the middle of the series.
This is the median. 2, 19, 44, 44, 44, 51,56, 78, 86, 99, 99.Step 6: Find the middle two numbers.
For example, 1, 2, 5, 6, 7, 8, 12, 15, 16, 17. The median is the number that comes in the middle of those middle two numbers (7 and 8), so that number would be 7.5 in this case. (To do this mathematically, add the two numbers together and divide by 2).

Tip:  You can have more than one mode. For example, the mode of 1, 1, 5, 5, 6, 6 is 1, 5, and 6.

Maths career _ Food

Ratios make baking a piece of cake

You’ve got your eggs, your butter, your flour, your sugar and chocolate. You’ve got your gran’s best recipe for chocolate cake. You’re all ready and all set to cook - and then trouble strikes. The recipe’s all in ounces and pints and you can’t find a set of scales anyway. What do you do? Add the secret ingredient, ratio..

Flour, eggs, sugar and butter are the main ingredients in baked treats - that includes biscuits, bread, pastry and cakes. The magic which changes these raw ingredients into a baker’s product comes from ratios (and a bit of heating).

Flour and eggs both contain proteins, long molecules which get tangled up in each other. These give structure and hold things together.

Moistness comes from the fat in the cake - which could be butter or oil - and the sugars. These sticky substances do the opposite and soften the food, making it crumbly.

So if you have too much butter and sugar, your (for example) cake may fall apart or stay runny. On the other hand if you put too much flour and egg in, the cake will be dry and tough. When making up a recipe bakers know which proportions they must mix their ingredients to get a good basic texture. Then fine tuning comes in to make the difference between a delicate crumbly walnut cake and a sticky carrot cake.

Weighing it up

So what are these balances you should be aiming for? Well, after millennia of baking, this is what has been found to work:

Cakes are made by combining 1 part sugar with 1 part butter or other fat, 1 part flour, and 1 part eggs. After a good beating to get lots of air inside the mixture, this makes a batter which will rise to be soft and moist.Biscuits, on the other hand, just require 1 part sugar, one part fat, and one part flour.While to make pancakes, you need 2 parts liquid (usually milk), 2 parts egg and 1 part flour.

Remember; measurements are by weight, not volume!

You can also convert a regular recipe - maybe a family speciality - into a ratio form using the techniques you learn in maths. But why would you want to do that?

Rationing is good for you

Cooking using ratios is much easier than working from a set recipe. It means that:

you can work without scales if you haven’t got anyyou can scale up and scale down recipes really easily. No need to recalculate everything if you’ve only got one egg - or only one friend coming round.ingredients can be substituted in and out easily - sunflower spread instead of butter for vegans, or rice flour instead of flour for coeliacsthe numbers are nice whole numbers, easy to remember

Bringing your maths into the kitchen can give you tasty results and liberate you from slavishly following recipes.

Benefits of vedic maths

Vedic Math is a delightful learning for children and adults. It helps in developing Math interest in children and helps them to improve accuracy , speed, sharpen focus and mental faculties. It enables the children to adopt creative math problem solving strategies.

Some of the benefits of practicing Vedic Math are as follows:

Learn strategies that make "Math An Art". As children enjoy Art so they enjoy Math.Speed and accuracy level of numerical computation becomes high.Follows the ideal natural system of mental math. As the mind thinks, recognises and articulates numbers from    Left to Right, so we do computation from Left to Right.Supplemental to current system of school math.Helps in achieving academic success.Vedic Math strategies are useful throughout the life.Helps in developing Math intuition. A student sees the question and the answer flashes in the mind in seconds.Vedic Math learning covers not only cover basic numeracy skills but also advanced math topics.

Maths in daily life

MATHS IN DAILY LIFE

1. When we get up we see the time of waking to verify whether we have enough time to
attend to various responsibilities. (Awareness of time, reading a clock / watch, planning
one’s routine.)
2. When we brush our teeth the life of the brush, its cost, the paste, its available quantity to
get new one come to one’s mind. (Cost accounting!)
3. In this connection, use of water, its availability, conservation, proper use of waste water
are relevant to think. (Awareness of environment, nature, preservation of the same)
4. Drinking coffee, tea, milk- the quantity, the temperature balance not affecting the tongue,
quantity consumable, proportion of mixes constituting milk, coffee powder or decoction,
boiling stage, filtering mechanism, washed cups / glasses ensuring health and a host of
things require analysis, reasoning and attention. (Practical knowledge of ratio and
proportion in domestic life also)
5. Same is the case with bathing. (water use and conservation)
6. When it comes to wearing of dresses, the size, the make, its durability, its condition￾washed and ironed with creases etc., need knowledge of proportion, geometry.
(Measurement of length, skill in transformation of cloth into clothe and other ideas
indicated)
7. Taking food as breakfast needs clear knowledge of proportion for preparation to have
good taste- more salt, chilly etc., besides spoiling the taste will affect health too as proper
balance has to be maintained

FRACTION

A fraction is a part of a whole

Slice a pizza, and we get fractions:

¹/₂¹/₄³/₈

(One-Half)

(One-Quarter)

(Three-Eighths)

The top number says how many slices wehave. 
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Click the pizza →

Slices we have:

Total slices:

"One Eighth"

Slices:

▲▼

Equivalent Fractions

Some fractions may look different, but are really the same, for example: 

⁴/₈=²/₄=¹/₂(Four-Eighths) (Two-Quarters) (One-Half)==

It is usually best to show an answer using the simplest fraction ( ¹/₂ in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

NumeratorDenominator

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

¹/₄+¹/₄=²/₄=¹/₂(One-Quarter) (One-Quarter) (Two-Quarters) (One-Half)+==One-quarter plus one-quarter equals two-quarters, equals one-half

ALGEBRAIC IDENTITIES

ALGEBRAIC IDENTITIES

Let us recall the following algebraic identities is earlier.

(a + b)² = a² + 2ab + b^2.                                    (a – b)² = a² – 2ab + b^2.                                  (a + b) (a – b) = a² – b^2.                                    (x + a) (x + b) = x² + (a + b) x + ab

Ex. Expand each of the following :

(i) (2x + 3y)²

(ii) (4x – 5y)²

(iii) (x + 5) (x + 6)

(iv) (x – 3) (x – 5)

Sol. (i) (2x + 3y)^2.=                               (2x)² + 2.2x.3y + (3y)²                             b   [∵ (a + b)² = a² + 2ab + b²]

= 4x² + 12xy + 9y²

(ii) (4x – 5y)² = (4x)² + 2.4x.5y + (5y)2                        [∵ (a – b)² = a²– 2ab + b²]

= 16x² – 40xy + 25y²

(iii) (x + 5) (x + 6) = x² + (5 + 6)x + 5.6               [∵ (x + a) (x + b) = x² + (a + b) x + ab]

= x² + 11x + 30

(iv) (x – 3) (x – 5) = {x + (–3)} {x + (–5)}            [∵ (x + a) (x + b) = x² + (a + b) x + ab]

= x² + {(–3) + (–5)}x + (–3).(–5) = x² + (–3 – 5)x + 15.                                                  = x² – 8x + 15

Ex. Find the product using appropriate identities :

(i) (x + 8) (x + 8)

(ii) (3x – 2y) (3x – 2y)

(iii) (x + 0.1) (x – 0.1)

Sol. (i) (x + 8) (x + 8) = (x + 8)^2.                       = x²+ 2(x) × 8 + (8)² = x² + 16x + 64.

(ii) (3x – 2y) (3x – 2y) = (3x – 2y)²                          [∵ (a – b)² = a² – 2ab + b²]

= (3x)² – 2(3x) × 2y + (2y)^2.                             = 9x² – 12xy + 4y².

(iii) (x + 0.1) (x – 0.1) = (x)2 – (0.1)²                       [∵ (a + b) (a – b) = a² – b²]

= (x)² – 0.01