Question

Which number below is irrational?
A. 3 √ 8
B. 3√ 125
C. √ 49
D. √ 52

Answer 1

The irrational number is
`√(52)`.

Explanation:

An irrational number is a non-terminating decimal number that does not follow any specific pattern (example: 0.333.... and 16.111... are all repeating with 3s and 1s, making them rational. While
`√(3)` or
`√(5)` are continuing decimals without a pattern, making them irrational).
`\sqrt[3]{8}`,
`\sqrt[3]{125}`, and
`√(49)` are all rational numbers, as they are equivalent to 2, 5, and 7 respectively.
`√(52)` can be written as
`√(4*13)` or
`2√(13)`, since
`√(13)` is not a complete square root, which means that
`2√(13)` is an irrational number.

Answer 2

D. √ 52 = 2 * √ 13 irrational

Explanation:

A. 3 √ 8 = 2 rational

B. 3√ 125 = 5 rational

C. √ 49 = 7 rational

D. √ 52 = 2 * √ 13 irrational