Class 10 -Prove √3 is a Irrational number.

 

Prove √3 is a Irrational number.

Proof:

Let √3 be a rational number.

So, $\sqrt{3}=\frac{\mathrm{p\; \_\_\_\_\; (1)}}{q}$

On squaring both sides

$3=\frac{p^2}{q^2}$
$q^2=\frac{p^2}{3}$

$\Rightarrow \mathrm{3 is\; a\; factor\; of}$$p^2$

$\Rightarrow \mathrm{3\; is\; a\; factor\; of\; p.}$

Now, again let p = 3 c.

So, $\sqrt{3}=\frac{\mathrm{3\; c}}{q}$

On squaring both sides
$3=\frac{\mathrm{9\; c}{}^{}}{q^2}$
$q^2=\mathrm{3\; c}{}^{}$
$c^2=\frac{q^2}{3}$
$\Rightarrow \mathrm{3\; is\; factor\; of}$$q^2$
$\Rightarrow 3$ is a factor of q.

Here 3 is a common factor of p, q  both

 So p, q are not co-prime.

Therefore our assumption is wrong. 

√$\sqrt{3}$ is an irrational number.

Class 10 -Prove √5 is a Irrational number.

 

Prove √5 is a Irrational number.

Proof:

Let √5 be a rational number.

So, $\sqrt{5}=\frac{p}{q}$

On squaring both sides

$5=\frac{p^2}{q^2}$
$q^2=\frac{p^2}{5}$

$\Rightarrow 5$ is a factor of $p^2$

$\Rightarrow 5$ is a factor of p.

Now, again let p = 5c.

So, $\sqrt{5}=\frac{5c}{q}$

On squaring both sides
$5=\frac{25c^2}{q^2}$
$q^2=5c^2$
$c^2=\frac{q^2}{5}$
$\Rightarrow 5$ is factor of $q^2$
$\Rightarrow 5$ is a factor of q.

Here 5 is a common factor of p, q  

 So p, q are not co-prime.

Therefore our assumption is wrong. 

√$\sqrt{5}$ is an irrational number.

Mutual Fund Vs Fixed Deposit

 

Here what I write or discuss is based on my  experience it is not to convince anyone to follow my Strategies it is only to strengthen my belief in myself, but this may give you some idea or. information because learning from others experience is best learning. 

This is very burning question now a days that one should take mutual fund or Fixed Deposit. 

To my mind Fixed deposit is better for those who are retired and are habitual to look into their portfolio again and again. 

If you look into your  portfolio again and again then fixed deposit is better for you. 

As for as mutual fund is concerned , it is better for those who are stable by observing regular ups and downs of the portfolio. 

One should konow that market gives average return not fixed return . We can obseve positive return in some years and negative return in some other years but average return of  three  to five years is generally positive. 

In the long run mutual fund  gives positive and higher return.So mutual fund is always better i

f you want to make money in the long run. 

You want to beat Inflation. 

You have patience. 

You are not habitual to witness your portfolio again and again, 

You have separate separate emergency fund. 

You are investing at least for 15 to 20 years, 

If  your answers are yes then NV follow the Mutual Fund. 

Bill of Credit Card

Bill of Credit Card 

Here what I write or discuss is based on my  experience it is not to convince anyone to follow my Strategies it is only to strengthen my belief in myself, but this may give you some idea or. information because learning from others experience is best learning. 

How to deal with the over credit card bill? 

Credit card gives us wonderful facility  to spend money easily according to the limit. This comforts is dangerous also. Sometimes we forget to calculate the bill amount and when we face over bill amount then we become very perplexed  and disturbed. 

Money App

Now a days many mony apps are there which gives you the facility to load the money from credit card to the Wallet then from Wallet to the bank account. 

Sometimes Relax Mind is Dangerous Also. 

When one come across this facility then generally one does not think very much before expending the money and in this way one is trapped in the vicious circle of borrowing the money from the Credit Card and filling the bill of the Credit Card. 

Pragmatism View. 

One must have tangible thinking regarding  the expenditures. One should have proper calculations before expenditures through Credit Card. It will be better write your important expenditures and the expenditures which can wait for some time. Focus on the important one only. 

Proper Calculations

Have proper Calculations and have proper estimation that how much bill you can fill comfortably . This means to say expenditures must be within the limit. 

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CASH TRANSFER FROM CREDIT CARD TO BANK ACCOUNT

CASH TRANSFER FROM CREDIT CARD TO BANK ACCOUNT 

Here what I write or discuss is based on my  experience it is not to convince anyone to follow my Strategies it is only to strengthen my belief in myself, but this may give you some idea or. information because learning from others experience is best learning. 

Now we will understand  how to manage cash for at the time of our need. This is very good facility of the credit card or different Apps. 

Yes there is some fee for this. First we choose an App like PayZapp, Paytm.... etc

Now after registration first load money from Credit Card to the Wallet then we transfer fund from Wallet to the Saving Account. 

It is not free, there is some fee for this according to norms of the Government and Bank. This facility can fulfill our needs, and this facility can make  us happy but it may gives us deep blow also if we don't pay the bill on time. 

Mutual fund Vs Property 1

Here what I write or discuss is based on my  experience it is not to convince anyone to follow my Strategies it is only to strengthen my belief in myself, but this may give you some idea or. information because learning from others experience is best learning. 

 It is very difficult decision that where one should invest in the Mutual Fund Or Property? Many people are puzzled in taking such decision. 

Generally both investment options are for long time. Financial Experts advise for long time investment in Mutual Fund and Property. 

Long time investment means atleast for 20 years. Here one should know that there is need of much amount for investing in Real State where one can starts investing in Mutual Fund by little amount also. 

Now investigate this question based on some parameters  between both. 

PURPOSE

First think what is your aim. Do you want property to live in or you want to earn return on your property? If you want property for your living then go ahead, without thinking much. If you wish to earn return on this, then go for Mutual Fund because in the long time there are chances that Mutual  Fund  may give you more return. 

LIQUIDITY

As for as liquidity is concerned then go for Mutual fund because mutual fund are more liquid then property. Property of little amount also takes much time to sell but mutual fund of  thousands crore may be sold in a second, so mutual fund are more liquid. 

SAFETY

Property is risky and to protect it guard it very hectic job but mutual fund are more secured and no need to worry about it.

CHANGEABLE

To change property is not possible easily. One will have to face much difficulty if one wants to change the property but you can sell one type of mutual fund in a second and can be purchased other type of mutual fund. 

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