#### The rational number among the following is _______.

√ 400 = √ (20 x 20)

= 20, which is a rational .

Hence, the rational number is √ 400.

#### Which of the following is an irrational number?

3259 is a prime number.

We know that the square of a prime number is always an irrational.

Hence, √ 3259 is an irrational number.

#### The smallest real number among 6√ 2 , 2√ 6, 2√ 3 and 4√ 3 is______.

Given, 6√2,2√6,2√3 and 4√3.

Expressing all the given numbers in the form of a, we get

√72, √24, √12 and √48

The smallest number=√12

=2√3

Hence, the smallest real number is 2√3.

#### Which of the following irrational numbers lies between 3 and 5?

Given, 3 and 5.

⇒√9 and √25

10, 11, 12, ... 24 lies between 9 and 25.

⇒√10, √11, √12,... and √24 lies between √9 and √25.

Hence, the required irrational numbers are √10 and √11.

#### The decimal expansion of 144/400 is ____

144/400=36/100

=0.36

Hence, the decimal expansion of 144/400 is terminating.

#### Which of the following is an irrational number that lies between 10/14 and 18/22?

Given rational numbers are 1014 and 1822.

1014=0.714285..... and 1822=0.81......

Between two rational numbers there are infinite irrational numbers.

Irrational numbers are non-terminating and non-repeating decimal numbers.

Hence, the required irrational number is 0.72034075264....

#### Which of the following is a rational number?

√2304=√(576×4)

=√576×4

=24×2

=48

Hence, √2304 is the rational number.

#### The largest real number among 2√3,4, √15 and 3√2 is ____.

Given, 2√3,4, √15 and 3√2.

Expressing all the given numbers in the form of √a, we get

√12, √16, √15 and √18.

The largest number=√18

=3√2

Hence, the largest real number is 3√2.

#### Which of the following irrational numbers lies between 3√2 and 2√3?

Given, 3√2 and 2√3.

Expressing the given numbers in the form of √a, we get

√18 and √12

13, 14, 15, 16 and 17 lies between 12 and 18.

⇒√13, √14, √15, √16 and √17 lies between √12 and √18.

Hence, the required irrational numbers are √13 and √14.

#### Which of the following irrational numbers lies between 4 and √21?

Given, 4 and √21.

⇒√16 and √21

17, 18, 19 and 20 lies between 16 and 21.

⇒√17, √18, √19 and √20 lies between √16 and √21.

Hence, the required irrational numbers are √17 and √18.

#### The value of π is approximately equal to 22/7.

The value of π is approximately equal to 22/7.

#### The rational number among the following is _____.

√4624=√(17×17×4×4)

=√(17×17×4×4)

= 17 × 4

= 68, which is a rational.

Hence, √4624 is the rational number.

#### If 1/13=0.076923, then 3/13=____.

Given, 1/13=0.076923.

3/13=3×1/13

= 3 × 0.076923

= 0.230769

∴3/13=0.230769

#### The decimal expansion of 35/80 is non-terminating and repeating.

35/80=0.4375,which is a terminating decimal.

Hence, the decimal expansion of 35/80 is a terminating decimal.

#### Which of the following is an irrational number?

√3125=√(625×5 )

=√625×√5

=25√5

The product of a rational number and an irrational number is irrational as long as the rational is not zero.

Hence, √3125 is an irrational number.

#### The difference of an irrational number and a rational number is an irrational number.

Consider an irrational number √2=1.41421...

√2−1=1.41421...−1

=0.41421...,which is an irrational number.

Hence, the difference of an irrational and a rational number is an irrational number.

#### Which of the following is an irrational number?

An irrational number is a non-terminating and non-recurring decimal.

Hence, 3.60555127... is an irrational number.

#### Which of the following is an irrational number?

An irrational number is a non-terminating and non-recurring decimal.

Hence, 2.64571311028843... is an irrational number.

#### Which of the following is an irrational number?

An irrational number is a non-terminating and non-recurring decimal.

Hence, 4.12310562561... is an irrational number.

#### The square root of a positive integer is a rational number.

√5=2.236067..., which is an irrational.

Hence, the square root of a positive integer need not be a rational number.

#### The number of rational numbers between any two consecutive whole numbers is ____.

The number of rational numbers between any two consecutive whole numbers is infinite.

#### Which of the following is an irrational number?

311 is a prime number.

The square root of a prime number is always an irrational number.

Hence, √311 is an irrational number.

#### Which of the following is an irrational number?

487 is a prime number.

The square root of a prime number is always an irrational number.

Hence, √487 is an irrational number.

#### The decimal expansion of a rational number is either terminating or non-terminating and recurring.

The decimal expansion of a rational number is either terminating or non-terminating and recurring.

#### √599 is a rational number.

599 is a prime number.

The square root of a prime number is always an irrational number.

Hence, √599 is an irrational number.

#### Every point on the number line is of the form √k, where k is a natural number.

−5 is a real number that exists on the number line, but it is not the square root of any natural number.

Hence, not every point on the number line needs to be of the form √k, where k is a natural number.

#### Which of the following is a rational number?

0.3333333... is a non-terminating and recurring decimal.

We know that,

a non-terminating and recurring decimal can be converted to the form of p/q, where p, q are integers and q ≠ 0.

0.3333333...=1/3

Hence, 0.3333333... is a rational number.

#### Which of the following is an irrational number?

521 is a prime number.

We know that the square root of a prime number is always an irrational.

Hence, √521 is an irrational number.

#### The number of rational numbers between two natural numbers is infinite.

The number of rational numbers between two natural numbers is infinite.

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