Is FOIL used to multiply radicals in sqrt{x - 3} • sqrt{x}?

In summary: So, you've answered your own question. Anything more you want to say about it?...and that's what you were looking for. So, you've answered your own question. Anything more you want to say about it?In summary, the conversation discussed the use of FOIL in multiplying radicals. It was explained that FOIL only works for two binomials and can cause confusion when applied to other types of expressions. The correct way to multiply radicals is to use the Distributive Property of Multiplication over Addition. It was also clarified that when multiplying radicals with different radicands, the product can be placed in one radicand.
  • #1
mathdad
1,283
1
The picture shows a simple problem. However, my question has to do with multiplication of radicals.

I know how to use FOIL.

sqrt{x - 3} • sqrt{x} is slightly confusing.

Do I multiply radicand times radicand?

My question is:

Does sqrt{x - 3} • sqrt{x} become sqrt{x^2 - 3x} in the FOIL process?

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  • #2
You're not being clear about how you are applying FOIL but $\sqrt x\sqrt{x-3}=\sqrt{x^2-3x}.$
 
  • #3
RTCNTC said:
The picture shows a simple problem. However, my question has to do with multiplication of radicals.

I know how to use FOIL.

sqrt{x - 3} • sqrt{x} is slightly confusing.

Do I multiply radicand times radicand?

My question is:

Does sqrt{x - 3} • sqrt{x} become sqrt{x^2 - 3x} in the FOIL process?

#1 Please forget you EVER heard of "FOIL". That silliness works ONLY with two binomials and simply has no other purpose. Some poor students ever refer to "reverse-foiling". This is madness. Just learn to multiply. That is WHY you found FOIL slightly confusing. You weren't using it on two binomials. This is exactly how it confuses FAR MORE students than it helps.

#2 $\sqrt{x-3}\cdot\sqrt{x}$ may not be quite as easy as that. Here's why...

$\sqrt{x^2} = |x|$

$\sqrt{x}\sqrt{x} = x$

You tell me why and you will have answered your own question.
 
  • #4
tkhunny said:
#1 Please forget you EVER heard of "FOIL". That silliness works ONLY with two binomials and simply has no other purpose. Some poor students ever refer to "reverse-foiling". This is madness. Just learn to multiply. That is WHY you found FOIL slightly confusing. You weren't using it on two binomials. This is exactly how it confuses FAR MORE students than it helps.

#2 $\sqrt{x-3}\cdot\sqrt{x}$ may not be quite as easy as that. Here's why...

$\sqrt{x^2} = |x|$

$\sqrt{x}\sqrt{x} = x$

You tell me why and you will have answered your own question.

Wish I could tell you what the difference is but I am so into the FOIL method. It's what I was taught back in high school in the 1980s.
 
  • #5
RTCNTC said:
Wish I could tell you what the difference is but I am so into the FOIL method. It's what I was taught back in high school in the 1980s.

Hey, if you have two binomials, you can FOIL all you want. What's your plan if you've one binomial and one trinomial? How about three binomials? Eventually, you'll have to abandon it, no matter how hard you try to hold on. Don't make excuses for bad teaching methods that we've already seen cause you confusion. When I first encountered FOIL, I think it was in the 8th Grade, I recall thinking "That's stupid. Why wouldn't I just multiply them? I've been multiplying polynomials since the 2nd grade." (Like 452.3 * 25.75 = ??) It's probably one of the things that got me into trouble that year - teaching other students how to multiply, rather than the rote memorization with extremely limited usage. There is a Distributive Property of Multiplication over Addition for ALL such operations.

What do we know about the nature of 'x' if $\sqrt{x}$ exists?

What do we know about the nature of 'x' if $\sqrt{x^{2}}$ exists?
 
  • #6
tkhunny said:
Hey, if you have two binomials, you can FOIL all you want. What's your plan if you've one binomial and one trinomial? How about three binomials? Eventually, you'll have to abandon it, no matter how hard you try to hold on. Don't make excuses for bad teaching methods that we've already seen cause you confusion. When I first encountered FOIL, I think it was in the 8th Grade, I recall thinking "That's stupid. Why wouldn't I just multiply them? I've been multiplying polynomials since the 2nd grade." (Like 452.3 * 25.75 = ??) It's probably one of the things that got me into trouble that year - teaching other students how to multiply, rather than the rote memorization with extremely limited usage. There is a Distributive Property of Multiplication over Addition for ALL such operations.

What do we know about the nature of 'x' if $\sqrt{x}$ exists?

What do we know about the nature of 'x' if $\sqrt{x^{2}}$ exists?

For sqrt{x}, x must greater than or equal to 0.

For sqrt{x^2}, x can be any integer.
 
  • #7
RTCNTC said:
For sqrt{x^2}, x can be any integer.

Actually, $x$ can be any real number.
 
  • #8
Okay, so what does that tell about whether \(\sqrt{x-3}\cdot\sqrt{x} = \sqrt{x^2 - 3x}\)?
 
  • #9
tkhunny said:
Okay, so what does that tell about whether \(\sqrt{x-3}\cdot\sqrt{x} = \sqrt{x^2 - 3x}\)?

It tells me that when two radicals with different radicands are multiplied, the product can be placed in one radicand.

So, sqrt{a} • sqrt{b} = sqrt{a•b}, as a general example.
 
  • #10
RTCNTC said:
It tells me that when two radicals with different radicands are multiplied, the product can be placed in one radicand.

So, sqrt{a} • sqrt{b} = sqrt{a•b}, as a general example.

With the same domain as the original implied domains!
 
  • #11
Great.
 

FAQ: Is FOIL used to multiply radicals in sqrt{x - 3} • sqrt{x}?

What is radical multiplication?

Radical multiplication is a mathematical operation that involves multiplying numbers with radical expressions, also known as square roots. It is used to find the product of two or more numbers that have a square root in them.

How do you perform radical multiplication?

To perform radical multiplication, you need to first simplify the radical expressions by finding perfect square factors. Then, multiply the numbers outside the radicals and the numbers inside the radicals separately. Finally, combine the two products to get the final answer.

What are some common mistakes when performing radical multiplication?

Some common mistakes when performing radical multiplication include forgetting to simplify the radicals, making errors in multiplying the numbers outside the radicals, and forgetting to combine the two products at the end.

What is the difference between radical multiplication and regular multiplication?

The main difference between radical multiplication and regular multiplication is that radical multiplication involves multiplying numbers with square roots, while regular multiplication involves multiplying whole numbers or fractions without any square roots.

In what situations is radical multiplication used?

Radical multiplication is commonly used in algebra and geometry to solve equations involving square roots and to find the areas of shapes with radical dimensions. It is also used in physics and engineering to calculate values involving square roots, such as velocity and acceleration.

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