Question

square root of 17

irrational square root of a nonperfect square
irrational terminating decimal
rational non-repeating /non-terminating decimal
irrational repeating decimal
irrational non-repeating/non-terminating decimal
irrational square root of a perfect square
rational square root of a nonperfect square
rational repeating decimal
rational terminating decimal
rational square root of a perfect square

Answer 1

The square root of 17 is an irrational number because 17 is not a perfect square. Therefore, its square root cannot be expressed as a simple fraction or a terminating decimal.

Here’s a breakdown of the terms you mentioned related to the square root of 17:

1. **Irrational square root of a nonperfect square**: **Yes**, since the square root of 17 is irrational.
2. **Irrational terminating decimal**: **No**, the square root of 17 does not have a terminating decimal representation.
3. **Rational non-repeating /non-terminating decimal**: **No**, this describes numbers like \(\pi\) or \(e\), not the square root of 17.
4. **Irrational repeating decimal**: **No**, repeating decimals are rational.
5. **Irrational non-repeating/non-terminating decimal**: **Yes**, the square root of 17 fits this description.
6. **Irrational square root of a perfect square**: **No**, because 17 is not a perfect square.
7. **Rational square root of a nonperfect square**: **No**, the square root of 17 is not rational.
8. **Rational repeating decimal**: **No**, the square root of 17 is not rational.
9. **Rational terminating decimal**: **No**, the square root of 17 is not rational.
10. **Rational square root of a perfect square**: **No**, the square root of 17 is not rational and 17 is not a perfect square.

In summary, the square root of 17 is an **irrational non-repeating/non-terminating decimal**.