Question

Найдите значение а , если а = √3√3√3√3√3....

Answer 1

$a = ( \sqrt{3} ) {}^{n}$
n - кол-во корней из 3

Answer 2

To find the value of 'a' in the expression you provided, we need to understand the pattern of the expression.

The expression is √3√3√3√3√3...

Notice that the expression is an infinite nested radical (√3√3√3...). To find 'a', we can set up an equation where 'a' is equal to the entire expression, including the radical:

a = √3√3√3...

Now, let's see if there's a pattern in the expression:

Let's square both sides of the equation:

a^2 = (√3√3√3...) ^ 2

On the right side, when we square the nested radical, it simplifies:

a^2 = 3√3√3...

But wait, the right side of the equation is the same as 'a'! So, we can rewrite the equation as:

a^2 = a

Now, we can solve for 'a':

a^2 - a = 0

a(a - 1) = 0

This equation has two solutions: a = 0 and a = 1. However, 'a' represents a positive value, so we discard the solution a = 0.

Therefore, the value of 'a' is:

a = 1