Question

please tell the answer ​

Answer 1

$\bf \huge \red{Answer}$

Note :

• The number which can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then the number is said to be rational number

• The number which is a type of real number and which can not written or can be converted to p/q form, where p and q are integers and q is a non-zero or which cannot be represented as a simple fraction. , then it is said to be irrational number.

Example :

$\bf{i) \sqrt {3} }$

• The √3 is an irrational number

Explanation :

• √3 is number which can not written or can be converted to p/q form, where p and q are integers and q is a non-zero or which cannot be represented as a simple fraction. , then hence it said to be irrational number.

$\bf{ii) \sqrt{9} }$

• √9 is a rational number

Explanation :

• √9 can be expressed in the form p/q, that is √9 = ±3 can be written in the form of a fraction 3/1. It show that √9 is a rational number.

$\bf{ iv)\sqrt{ {5}^{2} } }$

$\sf = > \sqrt{ {5}^{2} }$

$\sf{ = > \sqrt{5 \times 5} }$

$= > \sqrt{25}$

$\sf= > 5$

• 5 is rational number

Explanation :

• 5 is rational number which can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number and 5 is also a whole number, or integer. We know that All integers are rational numbers.

Answer 2

$\huge\tt\fcolorbox{cyan}{Lime}{ ANSWER♡࿐}$

(i) 21

Let us assume

21 is rational.

So we can write this number as

21 = ba ---- (1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by

2√ both sides, we get

1= ba√2

Now, divide by b, we get

b=a√2

or

√ab = √2

Here, a and b are integers so,

√ab is a rational number,

so,

√2 should be a rational number.

But,

√2 is a irrational number, so it is contradictory.

Therefore, √2

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$\sf\red{Thank\:you!}$

√1 is irrational number.