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# Powers and Roots - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Powers and Roots.

Printable worksheets containing selections of these problems are available here.

### Square Triangle

### Maundy Money

### Age of Augustus

### Square Percentage

### The Square of My Age

### The Square and the Root

### Pythagorean Quadruple

### Powers of Four

### Two in a Million

### Powerful Expressions

### Root Estimation

### Powerful Order

### Doubly Powerful

### Largest Expression

### Roots Near 9

### The Power of $x$

### Self-power Squares

### Power of 3

### Know Your Powers

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This is part of our collection of Short Problems.

You may also be interested in our longer problems on Powers and Roots.

Printable worksheets containing selections of these problems are available here.

Age 11 to 14

ShortChallenge Level

How many triangles have all three angles perfect squares (in degrees)?

Age 11 to 14

ShortChallenge Level

How much money did the Queen give away in pence as a power of 2?

Age 11 to 14

ShortChallenge Level

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

Age 11 to 14

ShortChallenge Level

What percentage of the integers between 1 and 10,000 are square numbers?

Age 11 to 14

ShortChallenge Level

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

Age 14 to 16

ShortChallenge Level

What is the remainder when the square of 49 is divided by the square root of 49?

Age 14 to 16

ShortChallenge Level

The sum of three square numbers equals $121$. What can those numbers be...

Age 14 to 16

ShortChallenge Level

Can you work out the value of x in this 'power-full' equation?

Age 14 to 16

ShortChallenge Level

What is the highest power of 2 that divides exactly into 1000000?

Age 14 to 16

ShortChallenge Level

Put these expressions in order, from smallest to largest.

Age 14 to 16

ShortChallenge Level

Which of these is the best approximation for this square root?

Age 14 to 16

ShortChallenge Level

Powers of numbers might look large, but which of these is the largest...

Age 14 to 16

ShortChallenge Level

To what power should $4^4$ be raised to give $8^8$?

Age 14 to 16

ShortChallenge Level

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Age 14 to 16

ShortChallenge Level

For how many integers ð‘› is the difference between âˆšð‘› and 9 is less than 1?

Age 14 to 16

ShortChallenge Level

Find the value of $x$ in this equation, where it appears in powers.

Age 14 to 16

ShortChallenge Level

How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?

Age 14 to 16

ShortChallenge Level

What power of 27 is needed to get the correct power of 3?

Age 14 to 16

ShortChallenge Level

Given these equations with unknown powers $x$ and $y$, can you work out $xy$?