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
sp2606 [1]
4 years ago
7

Prove that √2 + √3 is irrational​

Mathematics
1 answer:
Vika [28.1K]4 years ago
7 0

Step-by-step explanation:

Let √2 + √3 be a / b.

a and b are co - primes.

a and b have 1 as a common factor.

√2 + √3 = a / b

( √2 + √3 )^2 = ( a / b )^2

(√2)^2 + (√3)^2 + 2.√2.√3 = a^2 / b^2

2 + 3 + 2.√2.√3 = a^2 / b^2

5 + 2.√2.√3 = a^2 / b^2

2.√2.√3 = ( a^2 / b^2 ) - 5

2.√2.√3 = ( a^2 - 5b^2 ) / b^2

√2.√3 = ( a^2 - 5b^2 ) / 2b^2

a and b are not co - primes, as they more than 1 as a common factor.

So,

√2 + √3 is irrational.

Hence, proved.

You might be interested in
Martin is making a model of a Native American canoe. He has 9
monitta
Whats the rest of the quiestion
5 0
3 years ago
Please need help on this
Arisa [49]
Angle RQU would be obtuse
Angle SQU would be acute
7 0
3 years ago
PLEASEEEE help and explain!!
Citrus2011 [14]

Answer:

About 4% was his saving before tax

Step-by-step explanation:

8 0
3 years ago
Help me solve this problem!!
MariettaO [177]

Answer: Approximately 6573481.358 Hispanic businesses

Step-by-step explanation:

In 2009, the number of Hispanic owned businesses was 1.15 million

In 2013, the number of Hispanic owned businesses was 1.52 million

Since the growth is exponential, we would apply

Tt = ar^t-1

Where Tt is the number of Hispanic owned businesses after t years

a is the number of Hispanic owned businesses in 2009

r is the common ratio or exponential growth rate of the number of Hispanic owned business

at 2013 , t = 5(t= 0 in 2009 to t= 5 in 2013)

1520000 = 1150000 × r^5-1

1520000 / 1150000 = r^4

152/115 = r^4

1.32174 = r^4

Taking 4th root of both sides,

r = 1.07222

We want to determine the number of Hispanic owned business that would be there in 2034. It becomes

T2034 = 1150000 × 1.07222^25

T2034 = 1150000 × 5.7160

T2034 = 6573481.3579901

Approximately 6573481.358 Hispanic businesses

6 0
3 years ago
Read 2 more answers
-3/2+2 hi jjjjjjjjjjjjjjj
Lelechka [254]
Hi and hopes this helps:

Answer: 1/2

5 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following numbers belong to the set of complex numbers AND The set of imaginary numbers? Select all that apply.
    8·1 answer
  • The number can be divided by the least common multiple of 3 and 5
    8·1 answer
  • In one month Julian made 35 local phone calls and 20 long distance calls
    6·1 answer
  • 3+ 6x - x = 33<br> Can you find the answer
    10·2 answers
  • What is the width (or height) of the parking lot?
    10·1 answer
  • What is the distance between (4,-1) and (0,1)
    11·2 answers
  • Which shows 2 3/4 as a percent <br><br> A. 275%<br><br> B. 270% <br><br> C. 2.75%<br><br> D. 27.5
    6·1 answer
  • Find the Volume of the composite figure
    12·1 answer
  • Help please it important
    13·1 answer
  • What is the value of 12⁰?​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!