1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ankoles [38]
3 years ago
15

Why is it mathematically legal to multiply 2 √ 2 by √ 2 √ 2 in order to rationalize the denominator?

Mathematics
1 answer:
Gala2k [10]3 years ago
6 0
Well if you're referring to rationalizing \bf \cfrac{2}{\sqrt{2}}, which simply means, getting rid of the pesky radical at the bottom

well, it boils down to, hmm say... a quantity or even a polynomial, multiplied times 1, is itself, 2*1=2, 3*1 = 3, ducks*1 = ducks, spaghetti * 1 = spaghetti

or whatever * 1 = whatever
and the value of the multiplicand, doesn't change in anyway, is the same thing before and after the multiplication by 1

now....1 can also be a fraction  \bf \cfrac{2}{2}=1\qquad \cfrac{3}{3}=1\qquad \cfrac{1,000,000}{1,000,000}=1
\\\\\\
\cfrac{ducks}{ducks}=1\qquad \cfrac{spaghetti}{spaghetti}=1\qquad \cfrac{cheese}{cheese}=1
\\\\\\
\cfrac{\textit{the quick fox jumped}}{\textit{the quick fox jumped}}=1\qquad \cfrac{whatever}{whatever}=1

so.. when you're doing \bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\iff \cfrac{2}{\sqrt{2}}\cdot1

and the value multiplicand doesn't change in any way

now, try this in your calculator  \bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\\\\
-----------------------------\\\\
\textit{check how much is }\cfrac{2}{\sqrt{2}}\textit{ in your calculator}
\\\\\\
\textit{then check how much is }\sqrt{2}\textit{ in it}
You might be interested in
Find the product and express your answer in scientific notation. (1.3 x 10-6)(4 x 1010)
sveticcg [70]
(1.3\cdot10^{-6})(4\cdot10^{10})=(1.3\cdot4)(10^{-6}\cdot10^{10})=5.2\cdot10^{-6+10}\\\\=\boxed{5.2\cdot10^4}
3 0
3 years ago
Which formula represents this sequence
marysya [2.9K]

Answer:

pretty sure its b

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Find the volume of this prism:<br> 5 cm<br> 4 cm<br> 6 cm
nexus9112 [7]

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw EXAMPLE

put that into a formula.... and boom solved just comment on this for the answer

6 0
3 years ago
Help ill give brainlest pls
Citrus2011 [14]

Answer:

It is A

Step-by-step explanation:

Cuz it rotates Over the axis and reflect over it

8 0
2 years ago
Read 2 more answers
The tail on Alex‘s dog is 5 1/4 inches long this link is between which 2 inch marks on a ruler
wlad13 [49]
It's between the 5 and 6
6 0
3 years ago
Read 2 more answers
Other questions:
  • How do I solve for the area of the shaded part?
    12·1 answer
  • 8(3x-1)=-80 <br> ^^ also show the check pls
    15·2 answers
  • Which of the following statements demonstrates the associative property of multiplication?
    15·2 answers
  • The length of a rectangle is three times it’s width, the perimeter of the rectangle is 56cm , find the length and width
    8·1 answer
  • A construction worker has a rope that is 6 m long. She needs to cut it into pieces that are each 3/7 m long. How many such piece
    12·1 answer
  • katrina drinks 0.5 gallons of water per day. which expression shows how to find the number of cups of water she drinks in a week
    9·2 answers
  • The ratio of pages read to minutes for Hang is 5 : 8. Who has a greater ratio of pages read to minutes than Hang? Select all tha
    5·1 answer
  • There are 49 female performers in a dance recital. The ratio of men to women is 5:7. How many men are in the dance recital?
    9·1 answer
  • HELP I NEED HELP ASAP
    6·1 answer
  • Lin Ying belongs to an athletic club. In 800 m races her times are normally distributed with mean 128 seconds and standard devia
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!