Simplifying Square Roots | Math with Mr. J - Free Educational videos for Students in K-12

Simplifying Square Roots | Math with Mr. J - By Math with Mr. J

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00:0-1	Welcome to Math with mr J . In this video
00:05	, I'm going to cover how to simplify square roots
00:08	and we have four examples that we're going to go
00:10	through together in order to get this down . So
00:14	let's jump in the number one where we have the
00:16	square root of 20 . Now 20 is not a
00:20	perfect square . So we're not going to get a
00:23	nice and clean cut hole number answer . So we
00:26	need to simplify , we can do this by looking
00:29	for factors of 20 that are perfect squares and then
00:33	find their square roots . For example , we know
00:36	that four times five equals 24 5 are factors of
00:41	20 . They go into 20 so to speak ,
00:45	four is a perfect square . So let's do this
00:48	in order to simplify the square root of 20 equals
00:53	the square root of four times 5 . Now the
00:59	multiplication or product property of square roots lets us split
01:05	this , meaning we can do this the square root
01:08	of four times the square root of five . That's
01:13	equivalent to the square root of 20 . It's equal
01:16	. We're not changing the value of the problem at
01:19	all . Now we can take the square root of
01:22	our perfect square four and we end up with ,
01:27	Well the square root of four is too bring down
01:31	our square root of five because we cannot simplify that
01:35	any further . So our simplified answer is two times
01:40	the square root of five or two square root five
01:44	. Let's try another one and move on to number
01:47	two where we have the square root of 32 .
01:50	So we need to think are there any factors of
01:53	32 that are perfect square ? So any numbers that
01:56	can go into 32 , so to speak , that
01:59	are perfect squares . If so we can simplify if
02:03	not . It's already in simplest form While we know
02:07	that 16 times two equals 32 and 16 is a
02:12	perfect square . So we can simplify the square root
02:16	of 32 Equals The Square Root of 16 Times two
02:23	. Let's split this . So we have the square
02:26	root of 16 Times The Square Root of two .
02:31	16 is a perfect square , so the square root
02:34	of 16 is four , so we end up with
02:38	four Times the square root of two or 4 square
02:43	root two . Or you can even say for route
02:46	to now two cannot be simplified any further . So
02:50	this is our final answer . As far as simplifying
02:54	the square root of 32 . Now I do want
02:57	to mention we can take another path to get to
03:00	that same answer for number two . I'm going to
03:03	try to squeeze it in to the left here .
03:06	We know that four times eight also equals 32 4
03:10	is a perfect square . So this is the other
03:13	path we can take and I'm going to start by
03:16	splitting these just to make sure I have enough room
03:19	. So we have the square root of four times
03:23	the square root of eight . The square root of
03:27	four is too Let's bring down our square root of
03:31	eight . Now we can continue to simplify . We're
03:35	not done yet because we have a perfect square within
03:39	eight as far as factors go , because four times
03:42	two equals eight and four is a perfect square .
03:45	So again we can continue to simplify . So we
03:49	have two times the square root of four Times The
03:56	Square Root of two . So the square root of
03:59	four again is too , so we end up with
04:02	two times two times the square root of two .
04:07	Now the square root of two is simplified , so
04:10	we can't break that down any further but we can
04:13	multiply our two times two . So two times two
04:17	gives us four And then we have the square root
04:21	of two . So same exact answer but a different
04:25	path . And that's okay . Both of those paths
04:28	are correct . So keep that in mind . There
04:30	may be different paths as far as simplifying as square
04:34	root . Just always remember to check if you can
04:37	simplify further . Let's move on to number three and
04:40	try another one where we have the square root of
04:43	45 . So think any factors that are perfect squares
04:48	, yes , nine and five or factors of 45
04:51	9 times five equals 45 9 is a perfect square
04:56	. So the square root of 45 equals The Square
05:00	Root of nine Times 5 . Let's split this .
05:05	So square root of nine times the square root of
05:10	five . So the square root of nine is 3
05:15	. Bring down our square root of five . That
05:18	cannot be simplified any further . So we have three
05:22	times the square root of five or three square root
05:26	five or three . Route five . Lastly number four
05:30	, we have the square root of 75 . So
05:33	any factors that are perfect squares , Well , and
05:38	three are factors of 75 . times three equals 75
05:43	and 25 is a perfect square . So the square
05:47	root of 75 equals the square root of 25 times
05:54	three . Let's split . So we get The square
05:59	root of 25 Times The Square Root of three .
06:04	Now the square root of 25 is five , So
06:07	we have five and then the square root of three
06:12	is in simplest form . So we can't break that
06:14	down any further . And this is our final simplified
06:19	answer . Now , I do want to mention that
06:21	we always put the number before the square root symbol
06:24	, as you can see in all four of our
06:27	final simplified answers . So for example , if we
06:30	were to put the three first , so the square
06:33	root of three Times the square root of 25 and
06:39	get the square root of three times five , you
06:44	would want to rearrange this . So you have the
06:47	number first and put the square root second . So
06:52	you can see that we have the number , then
06:54	the square root . So that's common practice and that's
06:58	how you would want to leave your answers . So
07:01	there you have it . There's how you simplify square
07:04	roots . Now I would suggest really knowing the 1st
07:08	12 perfect squares . This is going to help a
07:11	lot as far as square roots go and simplifying them
07:15	. I have a pinned comment below with the 1st
07:19	12 . So if you need some help with those
07:21	, check that out . I also have some other
07:24	square root videos down in the description . I hope
07:28	that helped . Thanks so much for watching until next
07:32	time . Peace . Yeah . Yeah .

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