# Question 5caf9

Apr 10, 2017

Factor the rad a bit more....see below

#### Explanation:

$\sqrt{18} = \sqrt{2 \cdot 3 \cdot 3} = 3 \sqrt{2}$

Apr 10, 2017

color(red)(sqrt450=15sqrt2

#### Explanation:

$\sqrt{450} = 5 \sqrt{18}$

$\therefore \sqrt{2 \cdot 3 \cdot 3 \cdot 5 \cdot 5} = 5 \sqrt{2 \cdot 3 \cdot 3}$

$\therefore \sqrt{3} \cdot \sqrt{3} = 3$ and$\sqrt{5} \cdot \sqrt{5} = 5$

$\therefore 3 \cdot 5 \sqrt{2} = 3 \cdot 5 \sqrt{2}$

:.color(red)(sqrt450=15sqrt2#

Apr 12, 2017

#### Explanation:

If you follow the information in the answers from both Barney and Eddie together you will see that the first radical you provided is not the complete simplification, and you must do one more step.

It is the same as $\frac{32}{64} = \frac{2}{4}$, which is correct, but not the complete solution to the question. The answer is $\frac{1}{2}$ when simplified.

Apr 14, 2017

No.

#### Explanation:

Given radical can be presented in many forms

1. $\sqrt{450} = 5 \sqrt{18}$
2. $\sqrt{450} = 3 \sqrt{50}$
3. $\sqrt{450} = 15 \sqrt{2}$
4. $\sqrt{450} = \sqrt{450}$

As far as equivalence is concerned all four are equal.
However, the simplified radical, as per convention, is only appearing at number 3. The reason being

A. no perfect square factors other than $1$ in the radicand
B. The denominator is always rationalized so that no radicals appear in the denominator of a fraction.