SAT Math Part 4 - Solving Radical Equations and Plugging In Numbers - Free Educational videos for Students in K-12

SAT Math Part 4 - Solving Radical Equations and Plugging In Numbers - By The Organic Chemistry Tutor

Transcript


00:00	number 16 According to the equation shown below . What
00:06	is the value of X -7 squared ? So first
00:11	we need to calculate the value of X . And
00:14	then we can plug it into this expression to get
00:16	that value . So let's begin by adding 12 to
00:21	both sides . 28 plus 12 is 40 . Now
00:30	our next step is to divide both sides by five
00:35	40 , divided by five is 8 . So we
00:40	have this , The four fruit of x cubed is
00:43	equal to eight . Now what do you think we
00:45	need to do at this point ? What we need
00:48	to do is convert this radical expression into a fractional
00:52	exponents . So the four fruit of X cubed can
00:55	be written as x rays and three of the four
01:01	. Now we need to get X by itself .
01:04	So we need to get rid of this fractional exponents
01:08	. The best thing to do is to raise both
01:10	sides to the reciprocal of 3/4 , Which is going
01:14	to be 4/3 . So on the left side we
01:18	can see that the threes will cancel and the forest
01:21	will cancel . So X . Is equal to eight
01:26	. Race to the 4/3 . Now , how do
01:29	we evaluate this thing ? What is 8 ? Race
01:33	to the 4/3 ? Well , we need to do
01:36	is separate the four and 3 . We can say
01:39	this is eight . Race to the 1/3 . The
01:41	race to the 4th power . eight race of the
01:44	1/3 is basically the cube root of eight . One
01:48	number multiplied it by itself three times is eight ,
01:52	you know , two times two times two is eight
01:54	. So the cube root of eight is too .
01:56	So now we have two to the fourth power .
01:59	So we're multiplying 4 , 2s Two times two is
02:03	4 and four times 4 is 16 . So eight
02:07	race to the 4/3 is 16 . So now we
02:11	have the value of X . This is not the
02:14	final answer . Our goal is to calculate the value
02:20	of X -7 squared . So let's plug in accent
02:26	to the expression . So it's going to be 16
02:29	-7 squared 16 -7 is nine And nine squared is
02:35	81 . So this right here is my answer as
02:40	a choice . E . Number 17 . Which of
02:45	the following answer choices represents the value of Y .
02:49	If D is equal to three . Well , let's
02:53	begin marble . Place in D with three . So
02:59	now all we need to do is calculate the value
03:01	of why at this point now we can actually try
03:05	to solve it or we can plug in numbers .
03:09	So let's try answer choice be let's see if both
03:13	sides of the equation have the same value . If
03:16	why is equal to one . So let's replace .
03:19	Why with 1 ? three times one is stream 3
03:25	-5 is -2 . -3 is also negative too .
03:29	Now the square root of -2 is not equal to
03:32	-2 . So therefore we can eliminate answer choice B
03:39	. Let's try see . So we have three times
03:42	4 -5 and on the right side four monastery now
03:47	three times 4 is 12 And for ministry is one
03:52	, 12 -5 is seven . The square root of
03:55	seven does not equal one . So see is eliminated
04:00	. Let's try answer choice deep . Let's see if
04:02	Y is equal to seven . So we're going to
04:06	have three times seven minus five is equal to seven
04:09	. Monastery three times 7 is 21 , 7 -3
04:15	is four . Now 21 -5 is 16 And the
04:20	square root of 16 does equal four . So because
04:23	the left side is the same as the right side
04:26	. Answer choice D . Is the correct answer .
04:32	And now we're going to do at this point is
04:38	we're going to show our work just in case this
04:43	problem was a free response problem . So we're actually
04:47	going to solve this problem now , how should we
04:51	go about doing this ? So we have a square
04:54	root symbol on the left and no square root symbol
04:58	on the right because we have a radical function on
05:01	the left . We need to take the square both
05:02	sides just to get rid of it . So the
05:07	square of the square root of 3 , -5 ,
05:10	it's just gonna be three Y -5 . The square
05:13	root and the square will cancel . Now on the
05:16	right side , we need to foil . Why monastery
05:19	square ? So first let's expand the expression . So
05:24	why times why is why squared ? And then we
05:27	have y . times negative three Which is -3 Y
05:31	. And then we have another negative three Y .
05:33	And then negative three times negative three is positive nine
05:40	. Now let's combine like terms on the right side
05:44	. So negative three Y minus three . Y .
05:46	That's gonna be negative six Y . Next Let's add
05:51	5 to both sides And let's subtract both sides by
05:55	three wide . So we're going to have zero is
06:04	equal to y squared . Now a negative six Y
06:08	minus street Y . Is negative nine . Y .
06:11	And nine plus five is 14 . So that's what
06:14	we now have . So at this point we have
06:19	a try no meal with the leading coefficient of one
06:23	. So let's factor it will need to numbers that
06:25	multiply to 14 but add to the middle coefficient of
06:29	-9 . Now we know seven times two is 14
06:33	and seven plus two adds up tonight . But if
06:37	we use negative seven and negative two it's gonna add
06:40	up to negative nine but still multiply two positive 14
06:46	. So to factor the expression on the right It's
06:48	going to be why -7 Times Y -2 . Our
06:53	next step is to set each factor equal to zero
06:57	. So on the left we're going to add seven
06:59	on both sides . So this will give us the
07:02	answer that we have , which is why is equal
07:04	to seven . And on the right we're going to
07:07	add to the both sides which will give us another
07:10	potential answer why is equal to two now , because
07:13	we don't have that answer , we're not gonna worry
07:15	about it . But we can clearly see why D
07:18	is a correct answer choice based on what's written in
07:21	this problem . So that's it for this particular question
07:26	number 18 . If the square root of B is
07:29	equal to four , then what is the value of
07:32	the expression shown below ? So what we're gonna do
07:36	is we're going to calculate the value of B and
07:38	then plug it in to that expression . So what
07:43	is be equal to to get rid of the square
07:46	root symbol ? We need to take the square of
07:48	both sides . So the square of the square root
07:52	of B is just be so B is four squared
07:55	which means to be a 16 . So now we
07:58	can plug in 16 But we already know that the
08:01	square root of BS four so we can just replace
08:04	that with four . I'm gonna plug in . I'm
08:09	going to replace me of 16 on the right side
08:13	. four times 16 is 64 . Now the cube
08:17	root of 64 is going to be four Because if
08:22	you multiply 43 times You get 64 . So that's
08:28	the Cuban of 64 is for . So now we're
08:31	left with this four times four , four times 4
08:34	is 16 . So this is the answer which corresponds
08:39	to answer choice C . Number 19 . Let the
08:44	function age be defined by H . of X is
08:47	equal to seven x plus 25 . If the square
08:51	root of HF be over four is equal to nine
08:56	then what is the value of B . So here
08:59	we have a free response problem . So let's write
09:03	down what we know the square root of H .
09:07	of the over four is equal tonight . Using this
09:12	. How do we calculate B ? Well we know
09:15	that H . Of X . Is seven x plus
09:19	25 . So based on that , what is age
09:23	of be over 4 ? So in this case we
09:26	need to replace acts with the over four . So
09:29	it's seven times before plus 25 . So what we're
09:35	gonna do now is replace H . F . b
09:37	. of four with what we have here . So
09:41	now we have this equation . The square root of
09:44	seven times be over four plus 25 is equal tonight
09:51	. So now we're solving a radical equation . So
09:54	let's get rid of the square root by taking the
09:56	square both sides . So on the left side we're
09:59	gonna have seven times be over four Plus 25 .
10:03	And on the right side We have nine squared nine
10:06	Squared is 81 . Now let's subtract both sides by
10:11	25 , 81 -25 , 81 -20 is 61 and
10:21	61 -5 . That's going to be 56 . So
10:28	we have 56 is equal to seven Times be over
10:32	four . So let's multiply both sides by one of
10:35	the seven . So on the left side , the
10:39	seven and one of the seven will cancel . This
10:42	is the same as dividing both sides by seven .
10:45	On the right we have 56 divided by seven ,
10:47	which is eight , So be over four is equal
10:51	to eight . So now let's cross multiply four times
10:55	eight is 32 and that's equal to one times b
10:58	, which is B . So now we have the
11:00	answer B is equal to 32 . And so that's
11:04	it for this problem .

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