# Rational And Irratonal Square Roots

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| By Carlosvaras
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Carlosvaras
Community Contributor
Quizzes Created: 1 | Total Attempts: 242
Questions: 10 | Attempts: 243

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Please answer true or false to the statement.

• 1.

### The square root of 64 is irrational.

• A.

True

• B.

False

B. False
Explanation
The square root of 64 is not irrational. The square root of 64 is 8, which is a rational number because it can be expressed as a fraction (8/1). Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Since 8 can be expressed as a fraction and has a terminating decimal representation, it is not irrational. Therefore, the correct answer is false.

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• 2.

### The square root of 34.6 is rational.

• A.

True

• B.

False

B. False
Explanation
The square root of 34.6 is not rational because it cannot be expressed as a fraction of two integers. The square root of 34.6 is an irrational number, meaning it goes on infinitely without repeating and cannot be expressed as a simple fraction.

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• 3.

### The square root of 36 is rational.

• A.

True

• B.

False

A. True
Explanation
The square root of 36 is rational because it equals 6, which is a whole number and can be expressed as a ratio of two integers. In this case, 6 can be written as 6/1, making it a rational number.

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• 4.

### The square root of 81 is rational.

• A.

True

• B.

False

A. True
Explanation
The square root of 81 is rational because 81 is a perfect square. The square root of a perfect square is always a whole number, and whole numbers are considered rational numbers. In this case, the square root of 81 is 9, which is a whole number and therefore rational.

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• 5.

### The square root of 82 is rational.

• A.

True

• B.

False

B. False
Explanation
The square root of 82 is not rational because it cannot be expressed as a fraction of two integers. The square root of 82 is an irrational number, which means it cannot be written as a terminating or repeating decimal. Therefore, the correct answer is False.

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• 6.

### The square root of 72.6 is irrational.

• A.

True

• B.

False

A. True
Explanation
The square root of 72.6 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. The decimal representation of the square root of 72.6 goes on indefinitely without repeating, indicating that it is an irrational number.

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• 7.

### The square root of 25 is rational.

• A.

True

• B.

False

A. True
Explanation
The square root of 25 is rational because a rational number is any number that can be expressed as a fraction of two integers. In this case, the square root of 25 is 5, which can be expressed as the fraction 5/1. Therefore, it is rational.

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• 8.

### The square root of 50 is irrational.

• A.

True

• B.

False

A. True
Explanation
The square root of 50 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. It is a non-repeating, non-terminating decimal. The square root of 50 can be simplified as the square root of 25 times the square root of 2, which is 5 times the square root of 2. Since the square root of 2 is irrational, the square root of 50 is also irrational.

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• 9.

### The square root of 100 is irrational.

• A.

True

• B.

False

A. True
Explanation
The square root of 100 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. The square root of 100 is 10, which is a rational number, but it is also -10, which is also a rational number. Therefore, the square root of 100 has two rational solutions, making it irrational.

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• 10.

### The square root of 49 is irrational.

• A.

True

• B.

False

B. False
Explanation
The square root of 49 is not irrational because it is equal to 7, which is a rational number.

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• Current Version
• Mar 21, 2023
Quiz Edited by
ProProfs Editorial Team
• Oct 04, 2013
Quiz Created by
Carlosvaras

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