How do you simplify #sqrt(500/720)#?

Question

Eli Assouline · Accepted Answer

#=color(blue)(5/6#

We first simplify both terms individually by prime factorisation:

#sqrt(500) = sqrt(5*5*5*2*2) = sqrt(5^2 *5 *2^2) = 5 *2 sqrt5 =10sqrt5#

#sqrt(720) = sqrt(3^2 * 2^2 * 2 ^2*5) = 3*2*2sqrt5=12sqrt5#

Now our expression becomes: #(10sqrt5)/(12sqrt5)=(10cancelsqrt5)/(12cancelsqrt5)#

#=10/12#

#=color(blue)(5/6#

Nathan Axel · Answer

undefined To simplify sqrt(500/720), we can simplify the numerator and denominator separately.

First, let's simplify the numerator, 500. We can find the prime factorization of 500, which is 2^2 * 5^3.

Next, let's simplify the denominator, 720. The prime factorization of 720 is 2^4 * 3^2 * 5.

Now, we can simplify the fraction by canceling out common factors between the numerator and denominator.

After canceling out the common factors, we are left with sqrt(5/9).

Therefore, sqrt(500/720) simplifies to sqrt(5/9).

HIX Tutor · Answer

undefined Great question! Let's simplify $\sqrt{\frac{500}{720}}$ step by step.

1. **Can we break this into separate square roots?**
   - Yes! We can say: 
     $$
     \sqrt{\frac{500}{720}} = \frac{\sqrt{500}}{\sqrt{720}}
     $$

2. **Next, can we simplify $\sqrt{500}$?**
   - Yes! 
     $$
     500 = 100 \times 5
     $$
     So, 
     $$
     \sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}
     $$

3. **Now, can we simplify $\sqrt{720}$?**
   - Yes! 
     $$
     720 = 144 \times 5
     $$
     So, 
     $$
     \sqrt{720} = \sqrt{144 \times 5} = \sqrt{144} \times \sqrt{5} = 12\sqrt{5}
     $$

4. **Now let's put it all together.**
   - We have:
     $$
     \frac{\sqrt{500}}{\sqrt{720}} = \frac{10\sqrt{5}}{12\sqrt{5}}
     $$

5. **Can we simplify this fraction?**
   - Yes! The $\sqrt{5}$ cancels out. So we have:
     $$
     \frac{10}{12} = \frac{5}{6}
     $$

6. **So what is the final answer?**
   - The simplified form of $\sqrt{\frac{500}{720}}$ is:
     $$
     \frac{5}{6}
     $$

Does that all make sense?