Rewriting square root of fraction

TL;DR

The square root of 1/200 can be simplified to 1/10√2 or 1/20√2.

Transcript

• [Voiceover] So we have here the square root, the principal root, of one two-hundredth. And what I want to do is simplify this. When I say "simplify it" I really mean, if there's any perfect squares here that I can factor out to take it out from under the radical. And so I encourage you to pause the video and see if you can do that. Alright so the... Read More

Key Insights

• ❎ The square root of 1/200 can be simplified by factoring out perfect squares from 1/200, leading to the simplified form of 1/10√2 or 1/20√2.
• 🧑‍🏭 Factoring the number under the square root, 200, results in 2 × 2 × 5 × 5.
• 👻 Identifying the perfect squares in the factorization allows for the extraction of those values from under the radical.
• 🫚 Dividing the square root of 1/200 by the square root of 2 (multiplying by 1) eliminates the radical in the denominator.

Questions & Answers

Q: How can the square root of 1/200 be simplified?

To simplify the square root of 1/200, we can factor out perfect squares from 200. By factoring it as 2 × 2 × 5 × 5, we get 10√2.

Q: Can the square root of 1/200 be written in a different form?

Yes, the square root of 1/200 can also be written as 1/10√2 or 1/20√2. These forms are equivalent to the simplified expression.

Q: What if there are no obvious perfect squares in the factorization of 200?

If there are no immediate perfect squares, you can start by dividing by smaller numbers. Continuously dividing by factors until you find perfect squares will ultimately lead to the simplified result.

Q: How can the radical be eliminated from the denominator?

To remove the radical from the denominator, you can multiply both the numerator and the denominator by the square root of 2. This results in the expression 1/20√2, which can further simplify to 1/20 × 2 = 1/40.

Summary & Key Takeaways

• The square root of 1/200 can be simplified to 1/√200.

• By factoring out perfect squares, the square root of 200 can be simplified to 10√2.

• The final simplified form of the square root of 1/200 is 1/10√2 or 1/20√2.