Question

√3√3√3√3√3=3 to the power n

Answer 1

$\sqrt{3} \sqrt{3} \sqrt{3} \sqrt{3} \sqrt{3} = {3}^{n}$
$3 \times 3 \times \sqrt{3} = {3}^{n}$
$9 \sqrt{3} = {3}^{n}$
${3}^{2} \times {3}^{0.5} = {3}^{n}$

${3}^{2.5} = {3}^{n}$
so

n = 2.5

Answer 2

SOLUTION :

It is given in the question that,

$\sqrt{3} \times \sqrt{3} \times \sqrt{3} \times \sqrt{3} \times \sqrt{3} = {3}^{n}$

We know that,

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

So, we can write,

${( \sqrt{3} )}^{2} \times { (\sqrt{3} )}^{2} \times \sqrt{3} = {3}^{n}$

$3 \times 3 \times \sqrt{3} = {3}^{n}$

$9 \times \sqrt{3} = {3}^{n}$

$9 \times {3}^{ \frac{1}{2} } = {3}^{n}$

$9 \times {3}^{0.5} = {3}^{n}$

$9 = \frac{ {3}^{n} }{ {3}^{0.5} }$

$9 = {3}^{n - 0.5}$

${3}^{2} = {3}^{n - 0.5}$

Equating the exponents of both the sides, we get,

$2 = n - 0.5$

$2 + 0.5 = n$

$n = 2.5$

Hence,

Hence,The required value of 'n' is 2.5