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## Integrated math 1

### Course: Integrated math 1>Unit 13

Lesson 3: Simplifying square roots

# Simplifying square roots

Roots are nice, but we prefer dealing with regular numbers as much as possible. So, for example, instead of √4 we prefer dealing with 2. What about roots that aren't equal to an integer, like √20? Still, we can write 20 as 4⋅5 and then use known properties to write √(4⋅5) as √4⋅√5, which is 2√5. We *simplified* √20. Created by Sal Khan.

## Want to join the conversation?

• At , you added all the values and observed that if the sum was divisible by 3, so was the value. What video can I find this principle?
• At , Sal said that 117 is not a perfect square. What does that mean?
• A perfect square is a square root is not a decimal. You can not take the square root of 117 and have it not be a decimal. But if you were to take the square root of 9, it would be 3 because 3x3=9. Hope this helped!
• I'm having a LOT of trouble siplifying square roots and I can't understand why it's not making any sense to me...
The Square Roots Practice I can finish in about 10 seconds but I'm really hitting a wall with the Simplification side of Square Roots. Please help me!
• Wouldn't the answer to a square root really be positive and negative? For instance, if we wanted the square root of 9, it would be 3 and -3? because 3x3=9 and -3x-3=9?
• Yes, whenever you take square roots, you get two values (one positive and the other negative). But when you take the "principle" square root , you take only the positive value.
• Around , Sal explains that 5*3 and the square root of thirteen is 15 times the square root of thirteen. Why would you multiply the numbers 5 and 3?
• He is trying to simplify it. 5•3•√13 is more complex than 15•√13. The former has 3 steps involved (multiply 5 and 3, find square root of 13, multiply 15 by square root of 13), while the latter only has 2 steps involved (find square root of 13 and multiply by 15).
• Which video (and where) explains why you can add up the digits of a number to see if it's divisible by 3 like at - ?
• go to pre- algabra and in the factors and multiples section you will find divisablity tests at the top of the list and it explains the rule for 3 in the first video
• what is the concept of simplifying square roots? I don't understand square roots
• Roots are the inverse operation to powers. So if you take the square root of 6 and then you square it, then you would be left with 6 because the square and the square root cancel out.

Now if you have the square root of 2 plus the square root of 2, you would have 2√2. Notice that it isn't √4. It is actually 2√2 (which is the same as √8).

So the concept of simplifying square roots is like the concept of simplifying other things like exponents, parentheses, etc.
• Okay so how would you do fractions? I'm very confused and my math teacher sped through it so I didn't understand. How would you simplify the sqare root of 35 over 9 (just and example)?
• The thing about a square root of a fraction is that:
sqrt(35/9) = sqrt(35)/sqrt(9)
in other words, the square root of the entire fraction is the same as the square root of the numerator divided by the square root of the denominator. With that in mind, we can simplify the fraction:
sqrt(35)/3
As you can see, I left the numerator under the square root, because I can't simplify it, but the square root of 9 is three so I could replace the sqrt(9) in the denominator by 3.
The same rule applies to exponents: e.g. (2/3)^2=(2^2)/(3^2)