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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