What is the following quotient sqrt(120)/sqrt(30)?
Understand the Problem
The question is asking for the quotient of the two square roots, which involves simplifying the expression sqrt(120)/sqrt(30). We will carry out the division by simplifying the square roots and then finding the final value.
Answer
$2$
Answer for screen readers
The final answer is $2$.
Steps to Solve
- Simplify the square roots
Start by simplifying each square root separately:
- We have $\sqrt{120}$ and $\sqrt{30}$.
- Factor the numbers under the square roots
Factor $120$ and $30$ into their prime factors.
- $120 = 2^3 \cdot 3 \cdot 5$
- $30 = 2 \cdot 3 \cdot 5$
- Write the square roots in terms of their factors
Next, we can express the square roots with the prime factors: $$\sqrt{120} = \sqrt{2^3 \cdot 3 \cdot 5} = \sqrt{2^2 \cdot 2 \cdot 3 \cdot 5} = 2 \cdot \sqrt{30}$$
- Substitute into the original expression
So now we have: $$\frac{\sqrt{120}}{\sqrt{30}} = \frac{2\sqrt{30}}{\sqrt{30}}$$
- Cancel out common terms
Since $\sqrt{30}$ appears in both the numerator and the denominator, we can cancel them: $$\frac{2\sqrt{30}}{\sqrt{30}} = 2$$
The final answer is $2$.
More Information
The quotient of the two square roots simplifies to $2$, which shows that dividing two square roots can often be simplified much like dividing any fraction when you have common factors.
Tips
- Students might forget to simplify the square roots properly.
- Not identifying common factors in the numerator and denominator can lead to incorrect final results. To avoid this, always factor out and simplify before dividing.
