Question with square roots??!?!?

Question

I have a problem like : √45, and it shows it simplified to 3√5. How did they get that? Can someone please give me an explaination? And if I have a problem like: √169, how would that be simplified like the first one? Thanks.

Answer 1

In this case, you're using factors of the number in the sq root which also have whole numbers as their square roots. For instance, 45 can be factored down to 5 x 9. So it's √(5x9). The square root of 9 is 3, so you can remove 3 from underneath the sq root. So you end up with 3√5.

The √169 is actually a lot easier than that though. √169 = 13.

Answer 2

Well you always want to simplify a square root with one number you know has a whole square root and one that does not. This is so because you always want to do simplify as best you can. So for square root 45, 9 is the largest perfect square to go into 45 so you should know the square root of 9 is 3. And 9*5 = 45, hence the simplification of 3 sqrt 5.

If you have sqrt 169, well that is a perfect square altogether, 13.

Answer 3

First they factored
sqrt(45) = sqrt(9 x 5)

This is then separated
sqrt(45) = sqrt(9) x sqrt(5) = 3 sqrt(5)

For other problems, look for perfect squares that will divide into the number. Similarly, you could completely factor the number and look for pairs of factors. Your second problem doesn't make a good example because 169 = 13^2, but let's try 252. You can easily see that you can factor out a 2 and then another 2,leaving 252 = 2 x 2 x 63. But 63 is obviously divisible by 3 and, in fact is divisible by 9. So now you have 252 = 2 x 2 x 3 x 3 x 7, which is as far as you can go.

Now you can group it as before
sqrt(252) = sqrt(2 x 2) x sqrt(3 x 3) x sqrt(7)

which yields

sqrt(252) = 2 x 3 x sqrt(7) = 6 sqrt(7)

Answer 4

It's easy, they did what's called factorization. You take the number under the square root sign and find all it's prime factors. in the case of the number 45, it has 3 prime factors, 3, 3, and 5. Since you looking for square roots, you know since you have 3 twice you can take one three out as a square root. So you are left with 3 square root of 5. And to double check Square 3 (9) and 9*5) should equal 45.

Answer 5

This stumped me for a while but you have to think of the number under the sq root.

45=9*5
so sqrt45=sqrt9 * sqrt5
= 3*sqrt5 (since sqrt9 simplifies to 3)

for your example: 169 I think the only divisors there are 169*1 or 13*13 (which makes 13 the simplified answer)

if your ex was sqrt176 then you could say 16*11=176
so sqrt16*sqrt11=sqrt176
4*sqrt11=sqrt176 (since 4 is the square root of 16)


Math is SO not easy for me so maybe someone will come around with a way to simplify that example though.

Answer 6

the square root of 169 = 13 because 13 x 13 = 169

square root of 45 = 5 x 9 then square root 9 which = 3 so you put the 3 outside of the square root

Answer 7

The root of 45 is the root of (9x5) if you think about it. That means, it equals (the root of 9) x (the root of 5).

To do the same for the root of 169, find a whole number that divides into 169 and see if it's the square of another whole number (clue: the only number that goes exactly into 169 is actually its square root so you can't simplify that one)

Answer 8

It's a simple method of factoring under the square root sign. (sqrt xyz) = (sqrt x) * (sqrt y) * (sqrt z), and that equation works with any number of factors. In the example you give, (sqrt 45) = (sqrt 9) * (sqrt 5), and you know the sqrt of 9 is 3, so it simplifies to 3*(sqrt 5). To get the answer for sqrt 169, just factor the number 169, and you can solve whatever "perfect square" number factors happen to come from it.

Answer 9

Since 45 is 9 x 5 you can remove the square root of 9 which is 3.
169 is equal to 13 x 13 so that is the square root.
✩

Answer 10

45 = 9 x 5
the 3's are taken out because they are a square root of 9.
3 ^ 2 = 9
3 x 3 =9
so you are left with 3 on the outside and the 5 still a part of the square root because something x something doesn't equal 5.