Question

Estimate the radical by identifying which two consecutive integers it falls between.

Answer 1

The radical given is,

`\sqrt[]{34}`

To resolve this, we will look for a perfect square will is smaller to the square root of 34 and a perfect which is larger than 34.

Therefore, the two squares are 25 and 36.

Hence,

`\sqrt[]{34}\text{ lies between }\sqrt[]{25}\text{ and }\sqrt[]{36}`

Then,

`\begin{gathered} \sqrt[]{25}=5 \\ \sqrt[]{36}=6 \end{gathered}`

Hence,

`\sqrt[]{34}\text{ falls between 5 and 6}`

which is,

`5<\sqrt[]{34}<6`

Final answer

`5<\sqrt[]{34}<6`