Brain Teasers and Puzzles 

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy…

We have:

   10^1⁄₁₀ or 2^1⁄₃

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1⁄₁₀)³⁰ or (2^1⁄₃)³⁰

   10^{1⁄₁₀ x 30} or 2^{1⁄₃ x 30}

   10³ or 2¹⁰

   1000 or 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
This is a very common sequence.

Answer
5.

The numbers represent the number of letters of the words ONE, TWO, THREE, etc. Therefore, the answer is the number of letters in the word EIGHT.

Workings

Hint
Think laterally.

Answer
In the ground!

Workings

Hint
This is a well known nursery rhyme.

Answer
AJCTA.

These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.