Question

Sqrt45a^5 simplified

Answer 1

$\sqrt{45a^5}$

[scomposition of 45]

$\sqrt{9*5*a^5}$

[9 = 3^2, must use this notation (not 3*3)]

$\sqrt{3^2*5*a^5}$

[We appy one of the proprieties of square roots]

$\sqrt{3^2}* \sqrt{5}*\sqrt{a^5}$

[now we semplify: we must take out as much as possible all the elements under roots]

[to do that, we must divide the esponent of each element with the index of square roots (2)]

so

$\sqrt{3^2}$, 2/2 = 1

$\sqrt{5}$, 1/2 = 0 with 1 of rest

$\sqrt{a^5}$, 5/2 = 2 with 1 rest

[well, after do that, we can take out the elements under tbhe square roots!]

The quotient of each division is the esponent of the element out of the root

The rest of each division is the esponent of the element under the root

so:

$3^{1}$ (quotient = 1, see the first operation) * $\sqrt{5}$ (rest = 1, see the second operation) * $a^{2}$ (quotient = 2, see the third operation) * $\sqrt{a^1}$ (rest = 1, see the third operation)

The final result is:

3 (=3^1) * a² * √5 * √a

3a²√5a

It's more intuitive and easy, but the explanation (necessary) is very long. If you have other questions, ask me here in the comments! Also sorry for my english, not so good!