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Is 8 squared a rational number?

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Rational numbers are the sum of two integers. It contains all integers and may be written as a fraction or a decimal. It is represented by the letter ‘Q.’ When you divide a rational number, the result is in decimal form, which might be either ending or recurring. Examples of rational numbers are 3, 4, 5, and so on, which may be stated in fraction form as 5/1, 8/1, and 11/1.

Irrational numbers are those that cannot be stated as fractions or integer ratios. It can be expressed in decimals with an infinite number of non-repeating digits after the decimal point. It is represented by the letter ‘P.’Any integer that is not a rational number is an irrational number. Irrational numbers may be expressed in decimals but not fractions, implying that they cannot be expressed as a ratio of two integers. Irrational numbers have an endless number of non-repeating digits after the decimal point.
An irrational number is a real number that cannot be represented by a ratio of integers.  for example.√5 is an irrational number, 

The decimal expansion of an irrational number is neither ending nor recurring. Irrational is defined as a number that does not have a ratio or for which no ratio can be stated, i.e. a number that can only be expressed by using roots. Irrational numbers, on the other hand, cannot be stated as a ratio of two integers.

Is 8 squared a rational number? 

Solution: 

Rational numbers are the numbers that can be expresses as in the form of p/q .or in the ration of two integers. It includes all the integers and can be represented in fractions as well as decimal .

A rational number is a sort of real number that has the form p/q where q ≠ 0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Therefore, 82 = 8 × 8 = 64, it can be expressed in form of p/q i.e 64/1.

Hence, yes 8 squared is a rational number .

Similar Questions

Question 1:  Is 7 squared a rational number? 

Solution: 

Rational numbers are the numbers that can be expresses as in the form of p/q or in the ration of two integers. It includes all the integers and can be represented in fractions as well as decimal .

A rational number is a sort of real number that has the form p/q where q ≠ 0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Therefore, 72 = 7 × 7 = 49 , it can be expressed in form of p/q i.e 49/1.

Hence, yes 7 squared is a rational number.

Question 2:  Is the square root of 7 a rational number?

Answer:

Here, the given number, √7 cannot be expressed in the form of p/q. Alternatively, 7 is not a prime number but a rational number. √7 is equal to 2.645751… which gives the result of non terminating and non recurring digit after decimal, and cannot be expressed as fraction.

So, √7 is not a rational Number.

Question 3: Determine whether 4.257257… is a rational number.

Answer:

A rational number is a sort of real number that has the form p/q where q ≠ 0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, 4.257257… has recurring digits.

Hence, 4.257257.. is a rational number.

Question 4: Is 9 squared a rational number?

Solution: 

Rational numbers are the numbers that can be expresses as in the form of p/q .or in the ration of two integers . It includes all the integers and can be represented in fractions as well as decimal .

A rational number is a sort of real number that has the form p/q where q ≠ 0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here 9 is a rational number.

Therefore, 92 = 9 × 9 = 81, it can be expressed in form of p/q i.e 81/1

Hence, yes 9 squared is a rational number.

Question 5: Is √5 a rational number or an irrational number?

Answer:

A rational number is a sort of real number that has the form p/q where q ≠ 0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √5 cannot be expressed in the form of p/q. Alternatively, 5 is a prime number or rational number.  

Here, the given number √5 is equal to 2.23606.. which gives the result of non terminating and non recurring decimal, and cannot be expressed as fraction.

So, √5 is Irrational Number.

Question 6: Determine whether the product of √3 × √5 is rational or irrational?

Solution:

Given: √3 × √5 both are irrational numbers but it is not necessary that the product of two irrational number will be irrational.

Therefore, √3 × √5

= √15

But here square root of 15 is 3.8729833… which is non terminating and non recurring after decimal.

Hence, the product of √3 × √5 is irrational.


Last Updated : 28 Feb, 2024
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