Question

Determine if the root is a rational or irrational number. Explain your reasoning. ​Part A ​ 62−−√ ​ ​ ​Part B ​ 100−−−√3 ​

Answer 1

√62: irrational

√100: rational

Explanation:

A number is rational if it can be written in the form of: p/q, where p and q are integers.

Look at √62. This is about 7.87, but this is just an approximation; in fact, we can't write the exact value of √62 without actually writing "√62". Because of that, √62 cannot be written as p/q and is thus irrational.

Now look at √100. This is equal to 10, which can be written as 10/1, 20/2, 30/3, etc. Because it can be written in the form p/q, we know that √100 is a rational number.

Answer 2

Explanation:

Step 1: Determine if
`√(62)` is rational or irrational

`√(62)` →
`7.87400787...`

This number is irrational because the number never terminates so therefore, the number is irrational.

Step 2: Determine if
`√(100)` is rational or irrational

`√(100)` →
`10`

This number is rational because the number terminates and is a complete number therefore, the number is rational

Answer:
`√(62)` is irrational,
`√(100)` is rational