Question

what is the value of√9

Answer 1

In order to solve this exercise, you need to remember the following property for Radicals:

$\sqrt[n]{a}^n=a$

Notice that the Index "n" of the root and the exponent "n" inside the root are equal.

In this case you need to descompose the Radicand 9 into its Prime factors:

$9=3\cdot3$

According to the Product of powers property, when you multiply powers with the same base, you must copy the base and add the exponents. Then:

$9=3^2$

Rewrite the Radical and simplify:

$\sqrt[]{9}=\sqrt[]{3^2}=3$

The answer is:

$=3$