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
Viktor [21]
4 years ago
15

PLEASE HELP!!!!! How does “rationalizing the denominator” use the form of 1?

Mathematics
1 answer:
galina1969 [7]4 years ago
6 0
"Rationalizing the denominator" of a number is exactly what its title implies: turning its denominator into a rational number.

For an example, let's take the fraction 1/√2. We call √2 <em>irrational</em> because it cannot be expressed as a <em>ratio </em>of two integers. Oftentimes when we have irrational numbers like √2 in the denominator, it helps to perform a little bit of algebraic manipulation on them to make the denominator rational. Here's where that "form of 1" comes in. Remember that, as a rational number, 1 can be expressed as n/n, where n is any number. We can use this fact to rationalize the denominator of 1/√2 <em />by multiplying it by √2/√2, which is equivalent to 1.

When we multiply the two together, we get:

\frac{1}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}= \frac{\sqrt{2}}{(\sqrt{2})^2}= \frac{\sqrt{2}}{2}

Crucially, multiplying by 1 in the form of √2/√2 <em>keeps the fraction's value the same</em>, since 1 times any number just equals that same number. If we weren't multiplying but some form of 1, we'd change the number entirely, making the whole attempt at rationalizing the denominator pointless.
You might be interested in
Parallel lines have slopes that are
Tanzania [10]

Answer:

Equal

Step-by-step explanation:

8 0
3 years ago
What is the interquartile range (IQR) of this data set?<br><br> 2,6,7,11,15,16,17
CaHeK987 [17]

Answer: 10

Step-by-step explanation: First put numbers in numerical order

then divide your data and find the median of both sides

hope this helps mark me brainliest if it helped

6 0
3 years ago
Read 2 more answers
A watercolor painting is 20 inches long by 9 inches wide. Raymond makes a border around the watercolor painting by making a mat
sergey [27]

The mat adds 3 inches to each side, so the length would be 3+20 = 23 inches. The width would become 3 + 9 = 12 inches.Area = Length x width:

23 x 12 = 276 square inches

4 0
4 years ago
Complete the square x^2-10=16<br><br>​
Hatshy [7]

Answer:

(x - 5)² = 41

Step-by-step explanation:

* Lets revise the completing square form

- the form x² ± bx + c is a completing square if it can be put in the form

 (x ± h)² , where b = 2h and c = h²

# The completing square is x² ± bx + c = (x ± h)²

# Remember c must be positive because it is = h²

* Lets use this form to solve the problem

∵ x² - 10x = 16

- Lets equate 2h by -10

∵ 2h = -10 ⇒ divide both sides by 2

∴ h = -5

∴ h² = (-5)² = 25

∵ c = h²

∴ c = 25

- The completing square is x² - 10x + 25

∵ The equation is x² - 10x = 16

- We will add 25 and subtract 25 to the equation to make the

 completing square without change the terms of the equation

∴ x² - 10x + 25 - 25 = 16

∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides

∴ (x² - 10x + 25) = 41

* Use the rule of the completing square above

- Let (x² - 10x + 25) = (x - 5)²

∴ (x - 5)² = 41

3 0
3 years ago
. On a playground, there are 25
joja [24]
I think the answer is C
8 0
3 years ago
Other questions:
  • what is the area in feet of a parallelogram that has a base of 120 in and a height of 10 feet will mark brainiest
    7·1 answer
  • Use the drop-down menu to determine whether each phrase describes scalar or matrix multiplication.
    15·2 answers
  • I would love if someone could help me Thanks in advance
    15·1 answer
  • On the following number line the approximate locations of five real numbers are graphed
    9·2 answers
  • In a tennis tournament, there are 100 players. Each match is played between two players. The winner advances and the loser is el
    6·1 answer
  • Write a word problem to represent 2/5 × 1/2
    10·2 answers
  • Two more than 16 times a number is the same as 21 less than the product of -7
    11·1 answer
  • Find the answer when you substitute the letters with k = 14 and d = 5 in the equation. -5d - 7k.
    10·1 answer
  • HELP<br><br> Solve for the following equation showing all work step by step. 3646 = 1+5(4r+17)^3/2
    8·1 answer
  • The spinner has 3 options: Red, Blue, or Yellow. Jacob says
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!