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## Algebra basics

### Course: Algebra basics>Unit 1

Lesson 4: Square roots

# Simplifying square-root expressions: no variables

Sal simplifies sums and products of square roots. For example, he simplifies -√40+√90 as √10.

## Want to join the conversation?

• okay so how does 180 times 1/2 = the sqrt of 90 pls help  • All you're really looking for are square numbers that can be pulled out of the radical.
An important thing to realize is that sqrt(a•b) = sqrt(a)•sqrt(b). This allows us to separate the radical expression into it's factors. If it has any square factors, they simplify, and you're left with a simplified expression.
Here's an example with actual numbers:
sqrt(12) = sqrt(4•3) = sqrt(4)•sqrt(3) = 2sqrt(3)
• By , you can see the final answer, but I got 6√6 over 9. I got this by simplifying √128, then multiplying the whole fraction by √27 because a radical sign should never be on the denominator. Then after some simplifying, I got 6√6 all over the denominator 9. But I don't understand what I got wrong. Please help! • I'm going to try and repeat your steps...
1) `√128 = 8 √2` (I think your error could be here)
2) `8 √2 / √27 * (√27/√27)` = `8 √54 / 27`
3) `8 √54 / 27` = `8 √(9*6) / 27` = `8*3 √6 / 27` = `8 √6 / 9`

Either you didn't get the "8" out of √128, or you lost it somewhere along the way.

A couple of tips:
1) Try to reduce the fraction 1st. You can usually save your self quite a bit of work.
2) You did a better job then Sal in trying to get to a complete answer. Sal's answer would typically be considered incomplete as he didn't rationalized the denominator.

Any way, hope this helps.
• Why can't you just say √-40 instead of -√40? • Sorry if this has been asked, but:
Sal says sqrt180xsqrt1/2 is the same as 180^1/2 x 1/2^1/2. I don't understand why.

I've gone through the exponents unit before this, so I understand the concept that a square root is the reverse process (not including negatives here) of exponents. If that is the case, how can the sqrt180 be converted to 180^1/2 with sqrt1/2 converted to 1/2^1/2?

I also know that something in the whole equation is why it can be rewritten this way but I can't seem to figure that out on my own :( Please help me! • Um... I thought this was supposed to be a video about solving square roots with variables... why is it called that when that’s not what the topic is about? • At , when the answer is revealed as 8/3 times the square root of 2/3, can you simplify that even more (at when it is mentioned that 8 root 2 divided by 3 root 3 is an answer, can u simplify that to 8 root 6 over 9)? • I have a question regarding the method Sal uses here. When I look at Simplifying Square Roots, it reminds me a lot of Prime factorization.

In fact, I have been following along with these videos on Simplifying Square Roots, using the same method as I do with Prime Factorization (looking for divisibility by the smallest prime number).

My question: is there a specific reason Sal did not look for the smallest prime number here? Am I going to run into difficulties later on when looking for the smallest prime number while simplifying square roots? • When you simplify square roots, you are looking for factors that are perfect squares. Sal is factoring each number into perfect squares vs any remaining factors rather than going all the way down to prime factors. This just speeds things up a little bit.

However, you can use prime factorization. Find all the prime factors for the number inside the radical. Then, look for factor pairs. For example, where Sal used 4, with prime factorization you would look for and use 2*2.

Hope this helps.  