i have never seen the way he regrouped the numbers while subtracting. (at 2:25) how did he do that?

In American school, this is normally the way of regrouping you'll usually see. You probably already know that the lower math you have, the harder it is to teach, so instead of me TRYING to teach you it, here's a link that can help:https://www.khanacademy.org/math/arithmetic/arith-review-add-subtract/arith-review-subtract-within-100/v/introduction-to-regrouping-borrowing There you go! :)

Why cant you get a real value amount for the equation instead of a square root

When we have perfect squares, then square roots are easy. It is when we have imperfect squares such as 2,3,5 etc. that it gets more complicated. When taking imperfect squares, we end up in a part of numbers called irrational numbers - numbers that cannot be expressed as a fraction of two integers (thus are non-repeating). sqrt(2) is a real number, but it is also an irrational number and thus cannot be expressed in the way you want. However, for most real world problems, we can round an irrational number (like when we use 3.14 to approximate pi) to assist in calculations. However, anytime that we round, we loose accuracy, so sqrt(2) is more accurate than 1.414, so in Math which is can be more theoretical than real life, we just leave the sqrt(2) alone.

what do you do when you have to find out for B?

Rearrange the formula (a2+b2=c2) to isolate b: (c2-a2=b2). Now you can solve for b the same way you would for c. :)

Why do they always make the videos and why can't they make a written version that isn't just the video's script, is it too much work or something.

Well, the videos help visual learners more than just a written version, especially with geometry as you really can't get a grasp of some concepts without it being drawn out. In addition to videos, Khan Academy also has some articles scattered throughout the site. To answer your question: Yes, it would be too much work, because the limited KA team is spending effort reproducing already existing content instead of making new content.

what is meant by diagonal?

Draw a rectangle. Draw a line that splits the rectangle into two triangles. That line is a diagonal. Focus on one of the triangles. Notice that the triangle is a right triangle. You will find that the diagonal is the longest line in the triangle. (The definition of a diagonal is a line that connects two nonconsecutive vertices of a polygon.)

Can you break (√74)² down for me in steps? How do you solve that?

This is really just a one-step problem. The squaring undoes the process of taking the square root, so the answer is just 74.

In "Pythagorean theorem word problems" quiz there is an inscribed triangle question giving a result that requires you to find the square root of 4.5√. And find a result of: 2.121. Fair enough, but I can't figure out how to find the square root of a decimal number. Can anyone help me to understand it?

You could factor the √4.5 as √9 * √(1/2) which leaves you with (3√2)/2 but if you want a decimal answer there is certainly nothing wrong with just using your calculator when presented with something like that.

Are we just supposed to assume that the carpet has a right angle or was there some sort of math that told him that?

It is an assumption, but it's a fair one to make. Most quadrilateral carpets I've seen are squares or rectangles.

Main content

8th grade

Course: 8th grade > Unit 5

Lesson 4: Pythagorean theorem application

Pythagorean theorem word problem: carpet

Name: Pythagorean theorem word problem: carpet
Uploaded: 2011-02-20T16:28:47Z
Description: If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet.

Google Classroom

If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. Created by Sal Khan and Monterey Institute for Technology and Education.

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imad ali
Posted 10 years ago. Direct link to imad ali's post “what is meant by diagonal...”
what is meant by diagonal?
Button navigates to signup pageComment on imad ali's post “what is meant by diagonal...”
(2 votes)
Answer
- Sid
  Posted 10 years ago. Direct link to Sid's post “Draw a rectangle. Draw a ...”
  Draw a rectangle.
  Draw a line that splits the rectangle into two triangles.
  That line is a diagonal.
  Focus on one of the triangles.
  Notice that the triangle is a right triangle.
  You will find that the diagonal is the longest line in the triangle.
  
  (The definition of a diagonal is a line that connects two nonconsecutive vertices of a polygon.)
  Comment on Sid's post “Draw a rectangle. Draw a ...”
  (37 votes)
LorBuck
Posted 5 years ago. Direct link to LorBuck's post “i have never seen the way...”
i have never seen the way he regrouped the numbers while subtracting. (at
2:25
) how did he do that?
Button navigates to signup pageComment on LorBuck's post “i have never seen the way...”
(10 votes)
Answer
- connect17.mp
  Posted 5 years ago. Direct link to connect17.mp's post “In American school, this ...”
  In American school, this is normally the way of regrouping you'll usually see. You probably already know that the lower math you have, the harder it is to teach, so instead of me TRYING to teach you it, here's a link that can help:https://www.khanacademy.org/math/arithmetic/arith-review-add-subtract/arith-review-subtract-within-100/v/introduction-to-regrouping-borrowing
  
  There you go! :)
  Comment on connect17.mp's post “In American school, this ...”
  (7 votes)
Joshua Jimenez
Posted 7 years ago. Direct link to Joshua Jimenez's post “what do you do when you h...”
what do you do when you have to find out for B?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Alpha Juliet
  Posted 7 years ago. Direct link to Alpha Juliet's post “Rearrange the formula (a2...”
  Rearrange the formula (a2+b2=c2) to isolate b: (c2-a2=b2). Now you can solve for b the same way you would for c. :)
  Comment on Alpha Juliet's post “Rearrange the formula (a2...”
  (6 votes)
Brandonp1103
Posted 7 years ago. Direct link to Brandonp1103's post “Why cant you get a real v...”
Why cant you get a real value amount for the equation instead of a square root
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- David Severin
  Posted 7 years ago. Direct link to David Severin's post “When we have perfect squa...”
  When we have perfect squares, then square roots are easy. It is when we have imperfect squares such as 2,3,5 etc. that it gets more complicated. When taking imperfect squares, we end up in a part of numbers called irrational numbers - numbers that cannot be expressed as a fraction of two integers (thus are non-repeating). sqrt(2) is a real number, but it is also an irrational number and thus cannot be expressed in the way you want.
  However, for most real world problems, we can round an irrational number (like when we use 3.14 to approximate pi) to assist in calculations. However, anytime that we round, we loose accuracy, so sqrt(2) is more accurate than 1.414, so in Math which is can be more theoretical than real life, we just leave the sqrt(2) alone.
  Button navigates to signup page
  (2 votes)
alfdamanik
Posted 6 years ago. Direct link to alfdamanik's post “Would it be possible (if ...”
Would it be possible (if so is it easier?), if we made the equation as W²= (√74)²-7². Because technically it is the same thing right??
Button navigates to signup pageComment on alfdamanik's post “Would it be possible (if ...”
(5 votes)
Answer
- joshua574
  Posted 5 years ago. Direct link to joshua574's post “That is technically right...”
  That is technically right, but skipping steps can confuse you later on.
  Button navigates to signup page
  (1 vote)
heidi.cohen9
Posted 3 years ago. Direct link to heidi.cohen9's post “Can you break (√74)² dow...”
Can you break (√74)² down for me in steps? How do you solve that?
Button navigates to signup pageComment on heidi.cohen9's post “Can you break (√74)² dow...”
(2 votes)
Answer
- Ian Pulizzotto
  Posted 3 years ago. Direct link to Ian Pulizzotto's post “This is really just a one...”
  This is really just a one-step problem. The squaring undoes the process of taking the square root, so the answer is just 74.
  Button navigates to signup page
  (6 votes)
evgodbolt
Posted 2 years ago. Direct link to evgodbolt's post “wait how did he get 5?”
wait how did he get 5?
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(3 votes)
Answer
haley - samantha parisien
Posted 4 years ago. Direct link to haley - samantha parisien's post “Why do they always make t...”
Why do they always make the videos and why can't they make a written version that isn't just the video's script, is it too much work or something.
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Hecretary Bird
  Posted 4 years ago. Direct link to Hecretary Bird's post “Well, the videos help vis...”
  Well, the videos help visual learners more than just a written version, especially with geometry as you really can't get a grasp of some concepts without it being drawn out. In addition to videos, Khan Academy also has some articles scattered throughout the site. To answer your question: Yes, it would be too much work, because the limited KA team is spending effort reproducing already existing content instead of making new content.
  Comment on Hecretary Bird's post “Well, the videos help vis...”
  (4 votes)
Bengü Ergin
Posted 9 years ago. Direct link to Bengü Ergin's post “In "Pythagorean theorem w...”
In "Pythagorean theorem word problems" quiz there is an inscribed triangle question giving a result that requires you to find the square root of 4.5√. And find a result of: 2.121. Fair enough, but I can't figure out how to find the square root of a decimal number. Can anyone help me to understand it?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Thomas B
  Posted 9 years ago. Direct link to Thomas B's post “You could factor the √4.5...”
  You could factor the √4.5 as √9 * √(1/2) which leaves you with (3√2)/2 but if you want a decimal answer there is certainly nothing wrong with just using your calculator when presented with something like that.
  Button navigates to signup page
  (5 votes)
evelynabadger
Posted 8 months ago. Direct link to evelynabadger's post “Are we just supposed to a...”
Are we just supposed to assume that the carpet has a right angle or was there some sort of math that told him that?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Venkata
  Posted 8 months ago. Direct link to Venkata's post “It is an assumption, but ...”
  It is an assumption, but it's a fair one to make. Most quadrilateral carpets I've seen are squares or rectangles.
  Button navigates to signup page
  (4 votes)

Video transcript

A carpet measures 7 feet long and has a diagonal measurement of square root of 74 feet. Find the width of the carpet. So let's draw ourselves a carpet here. So let's draw a carpet. It has a length of 7 feet, so let's say that that is 7 feet, right there. And it's going to be a rectangle of some kind. So let's say that we're looking down on the carpet like that. That's our carpet. And then it has a diagonal measurement of square root of 74 feet. So that means that this distance, right here-- draw it a little bit neater than that --this distance right here, the diagonal of the carpet, is the square root of 74 feet. And what they want to know is the width of the carpet. Find the width of the carpet. So let's say that this is the width of the carpet. That is w, right there. Now, you might already realize that what I have drawn here is a right triangle. Let me make sure you realize it. This is a 90 degree angle here. And since that is a triangle that has a 90 degree angle, it's a right triangle. The side opposite the right angle, or the 90 degrees, is a hypotenuse, or the longest side. It is the square root of 74. And the shorter sides are w and 7. And the Pythagorean Theorem tells us that the sum of the squares of the shorter side will be equal to the square of the hypotenuse, so the square of the longer side. So we get w squared, this side squared. plus 7 squared, this other side squared, is going to be equal to the hypotenuse squared, square root of 74 squared. And then we get w squared plus 49 is equal to the square root of 74 squared. Well, that's just going to be 74. It is equal to 74. We can subtract 49 from both sides of this equation. So we have just a w squared on the left-hand side. Subtract 49 from both sides. The left side-- these guys are going to cancel out, we're just going to be left with a w squared --is equal to-- What's 74 minus 49? 74 minus 49, well, we can do a little bit of regrouping or borrowing here, if we don't want to do it in our head. We can make this a 14. This becomes a 6. 14 minus 9 is 5. 6 minus 4 is 2. And we have w squared is equal to 25. So w is going to be equal to the square root of 25, the positive square root. So let's take the square root of both sides, the positive square root, and we will get w is equal to 5. Because we obviously we don't want it to be negative 5. That wouldn't be a realistic distance. So the width of the carpet is 5. And we're done.