IIT JEE , AIEEE Forum - Mathematics , Algebra - A question on multiplication (yes u read it right on MULTIPLICATION!!!!) Just look inside.

oneyeartogo

3 * 2 = 3+3

We added 3 two times.

But how do u explain this:

$(\sqrt{3}) \;\;(\sqrt{2})$

What I mean to say is how do u add $\sqrt{3}$ to itself $\sqrt{2}$ times?

eshaan

$\sqrt{3}*\sqrt{2}=\sqrt{3*2}=\sqrt{3+3}=\sqrt{6}$

hehehehehehee!

rudra.panda

$\sqrt{3}*\sqrt{2}=\sqrt{3*2}=\sqrt{6}$

Same as eshaan

oneyeartogo

Oh I didn't think about that.

How about this one:

${2}^{\sqrt{3}}$

2 multiplied by itself $\sqrt{3}$ times!!!!

rudra.panda

2^ $\sqrt{3}$

={(2^ $\sqrt{3}$ )^ $\sqrt{3}$ }^1/ $\sqrt{3}$

=(2^3)^1/ $\sqrt{3}$

=8^1/ $\sqrt{3}$

thanks for pointing out the error.

allamraju

Rudra, $\sqrt[3]{8}$ =8^1/3 and not 8^1/rt3.Check your answer.

oneyeartogo

What I am really asking is how do u define multiplication (or exponents) for real numbers.

PULKIT.CHAMP

WELL BUDDIES.ALL QRERIES ARE SOLVED IN BOOK BERNALD AND CHILD

kislay

2^(root 3) means 2 multiplied to itself root 3 times..it is quite obvious.though seems quite odd but it is fact.

oneyeartogo

But then how did we calculate the value of ${2}^{\sqrt{3}}$ . Actually how did we multiply 2 to itself $\sqrt{3}$ times

kislay

it can be found with the help of log...

actually we multiply 2 to itself root 3 times while e find its value..

that's why we can't solve it directly and take help of log..
hope it is clear now

nadeemoidu

Consider some rational exponent.

2^2.5

This is equal to 2^5/2 = ${(\sqrt{2})}^5$ Which we know how to calculate.

Similarly, ${2}^{\sqrt{3}}$ = 2^1.732... = 2 ^1732/1000 = $\sqrt[1000]{2^{1732}}$

This is not the exact value , but this is how it is defined

Ask & Discuss Questions with Community & Experts

Rudra,=81/3 and not 81/rt3.Check your answer.

Rudra, $\sqrt[3]{8}$ =8^1/3 and not 8^1/rt3.Check your answer.