Rational And Irratonal Square Roots

1. The square root of 36 is rational.

True

False

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.

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.

2. The square root of 25 is rational.

True

False

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.

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.

3. The square root of 81 is rational.

True

False

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.

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.

4. The square root of 82 is rational.

True

False

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.

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.

5. The square root of 64 is irrational.

True

False

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.

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.

6. The square root of 34.6 is rational.

True

False

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.

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.

7. The square root of 49 is irrational.

True

False

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

Explanation

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

8. The square root of 72.6 is irrational.

True

False

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.

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.

9. The square root of 50 is irrational.

True

False

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.

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.

10. The square root of 100 is irrational.

True

False

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.

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.