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# Simplifying square roots of fractions

We can simplify the √(1/200) by finding perfect squares that are factors of 200. We could either look directly for the largest perfect square factor or break 200 into smaller factors and find repeated factors. If we have √2 in the denominator, we can multiply by √2/√2 to make an equivalent fraction.

## Want to join the conversation?

• At Sal says that sqrt(2) * sqrt(2) is 2. How does that work?
• We can multiply square roots.
sqrt(2) * sqrt(2) = sqrt(4)
What is the sqrt(4)? It = 2.
• I might be a little dumb but this just feels like overcomplicating things xd
• How on earth is ONE 200th equal to a 20th of the square root of 2?
The square root of 200 is equal to a 20th of the square root of 2. Not ONE 200th.
Please explain... I, and my calculator are both confused.
• I'm not sure what you mean.
1/200 ≠ √2/20
I know this immediately because the LHS is rational and the RHS is irrational so they cannot be equivalent. What makes you think that it was implied that they were equivalent?
• How does the square root of 2 times the square root of 2 equal 2?
• I wish he explained why he puts his symbols and numbers where he puts them. Why do you put the 10 on the outside of the radical and the 2 inside?
(1 vote)
• You can only bring items outside the radical if you can do the square root.
1) Sal starts with sqrt(200)
2) He splits it into sqrt(2)*sqrt(100)
-- The 2 is a prime number, and not a perfect square. So, it must stay inside the radical.
-- The 100 is a perfect square. 100 = 10^2. So you can do the sqrt(100) = 10. The 10 is now outside the square root.
-- Write the numbers in the correct order: numbers outside go first, then the remaining radical. This gives you: 10 sqrt(2)

Hope this helps.
• I understand square roots a lot better than most people in my class, but I'm stumped on how to simplify square roots this video made me a little more confused, can someone help break it down for me?
• Just prime factorize and find any perfect squares in the number. Then find the root of those perfect square and put that outside of the square root! I recommend making sure you are familiar with these terms as sal uses it alot in his later videos.
• i dont get it at all
• Can someone explain why the two in purple is separated from the other twos?
(1 vote)
• 200 factors into 2*2*2*5*5
When simplifying a square root, you need numbers that are squared to bring a value outside the radical. Notice, Sal pairs up the factors into (2*2)(5*5)(2). He can take the square root of (2*2), it becomes 2. He can take the square root of (5*5), it becomes 5. He can't take the square root of 2 (this is the purple 2) because there is only one 2. So, it stays in the radical.
Hope this helps.