Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Show that $square root of 3$ - $square root of 2$ is an irrational number.

hint Hint:

Hint:
The real numbers which cannot be expressed in the form of p/q(where p and q are integers and q ≠ 0) are known as irrational numbers. In the given question we are asked to prove if $square root of 3$ and $square root of 2$ is irrational number. To do so we use the method of contradiction.

The correct answer is: Is an irrational number

Let's assume that $square root of 3$ - $square root of 2$ is a rational number.
¶Step 1 of 2:
¶If $square root of 3 space end root$ - $square root of 2$ is rational, that means it can be written in the form of p/q, where p and q integers q ≠ 0.
¶So, $square root of 3 minus square root of 2 equals p over q$
¶Squaring both sides
¶ So, $left parenthesis square root of 3 minus square root of 2 right parenthesis squared equals p squared over q squared$
¶ $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 plus 2 minus 2 cross times square root of 3 cross times square root of 2 equals p squared over q squared end cell row cell 5 minus 2 square root of 6 equals p squared over q squared end cell row cell 5 minus p squared over q squared equals 2 square root of 6 end cell row cell fraction numerator 5 q squared minus p squared over denominator 2 q squared end fraction equals square root of 6 end cell end table$
¶Step 2 of 2:
¶Here, we see that $fraction numerator 5 q squared minus p squared over denominator 2 q squared end fraction$ is a rational number. But $square root of 6$ is an irrational number. So our assumption is wrong.
¶Final Answer:
¶As $square root of 6$ is an irrational number. So $fraction numerator 5 q squared minus p squared over denominator 2 q squared end fraction$ must also be an irrational number. Thus, our assumption is wrong. Hence, $square root of 3 minus square root of 2$ is an irrational number

Related Questions to study

Show that $square root of 2$ is an irrational number

Show that $square root of 2$ is an irrational number

Show that $square root of 3$ is an irrational number

Show that $square root of 3$ is an irrational number

Ramesh earns Rs. 40000 per month. He spends $2 over 5$ of his income on food, $5 over 12$ of the remaining on education of children and $3 over 7$ of the remainder on the house rent. How much money is still left with him?

Ramesh earns Rs. 40000 per month. He spends $2 over 5$ of his income on food, $5 over 12$ of the remaining on education of children and $3 over 7$ of the remainder on the house rent. How much money is still left with him?

parallel

Insert 3 rational numbers between the rational numbers $2 1 third$ 𝑎𝑛𝑑 $3 1 third$

Insert 3 rational numbers between the rational numbers $2 1 third$ 𝑎𝑛𝑑 $3 1 third$

Express 1.666666….. as a vulgar fraction.

Express 1.666666….. as a vulgar fraction.

Find 10 rational numbers between $3 over 5$ 𝑎𝑛𝑑 $3 over 4$

Find 10 rational numbers between $3 over 5$ 𝑎𝑛𝑑 $3 over 4$

parallel

Divide the sum of $13 over 5$ and $fraction numerator negative 12 over denominator 7 end fraction$ by the product $fraction numerator negative 31 over denominator 7 end fraction$ and $fraction numerator 1 over denominator negative 2 end fraction$

Divide the sum of $13 over 5$ and $fraction numerator negative 12 over denominator 7 end fraction$ by the product $fraction numerator negative 31 over denominator 7 end fraction$ and $fraction numerator 1 over denominator negative 2 end fraction$

Express 0.3178 in the form of p/q. Where p and q are integers.

Express 0.3178 in the form of p/q. Where p and q are integers.

One liter of petrol costs Rs. 70. What is the cost of 70 litres of petrol

One liter of petrol costs Rs. 70. What is the cost of 70 litres of petrol

parallel

Insert 3 rational numbers between 3 and 4

Insert 3 rational numbers between 3 and 4

Uma earns Rs. 16000 per month. She spends $1 fourth$ of her income on food, $3 over 10$ of the remainder on house rent and $5 over 21$ of the remainder on the education of children. How much money is left with her?

Uma earns Rs. 16000 per month. She spends $1 fourth$ of her income on food, $3 over 10$ of the remainder on house rent and $5 over 21$ of the remainder on the education of children. How much money is left with her?

Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal: $6 over 24$

Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal: $6 over 24$

parallel

In a school, $5 over 8$ 𝑡ℎ of the students are boys, if there are 240 girls, find the number of boys in the school?

In a school, $5 over 8$ 𝑡ℎ of the students are boys, if there are 240 girls, find the number of boys in the school?

If 24 pairs of trousers of equal size can be prepared with 54 m of cloth, what length of cloth is required for each pair of trousers?

If 24 pairs of trousers of equal size can be prepared with 54 m of cloth, what length of cloth is required for each pair of trousers?

Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal: $24 over 11$

Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal: $24 over 11$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.