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

Age 11 to 14 Short
Challenge Level

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

Mini Cross-number

Age 11 to 14 Short
Challenge Level

Which digit replaces x in this crossnumber?

Maundy Money

Age 11 to 14 Short
Challenge Level

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

Age of Augustus

Age 11 to 14 Short
Challenge Level

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

Tenth Power

Age 11 to 14 Short
Challenge Level

Do these powers look odd...?

Square Percentage

Age 11 to 14 Short
Challenge Level

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

The Square of My Age

Age 11 to 14 Short
Challenge Level

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

Megabytes and Kilobytes

Age 14 to 16 Short
Challenge Level

How many bytes are there in one megabyte?

Power up to 1000

Age 14 to 16 Short
Challenge Level

Find $x+y$, where $2^x\times5^y=1000$

The Square and the Root

Age 14 to 16 Short
Challenge Level

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

Pythagorean Quadruple

Age 14 to 16 Short
Challenge Level

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

Root 2017

Age 14 to 16 Short
Challenge Level

Between which two whole numbers is $\sqrt{2017}$ $?$

Powers of Four

Age 14 to 16 Short
Challenge Level

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

The Power of the Sum

Age 14 to 16 Short
Challenge Level

What is this sum, expressed as a power of 2?

Cube Factors

Age 14 to 16 Short
Challenge Level

How many factors of $9^9$ are perfect cubes?

Two in a Million

Age 14 to 16 Short
Challenge Level

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

How Many Squares?

Age 14 to 16 Short
Challenge Level

How many 4-digit numbers are perfect squares?

Huge Powers

Age 14 to 16 Short
Challenge Level

Can you put these numbers in order?

Powerful Expressions

Age 14 to 16 Short
Challenge Level

Put these expressions in order, from smallest to largest.

Root Estimation

Age 14 to 16 Short
Challenge Level

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

Rough Root

Age 14 to 16 Short
Challenge Level

Which of these options is closest to this square root?

Big Product

Age 14 to 16 Short
Challenge Level

How many digits are there in this product?

Powerful Order

Age 14 to 16 Short
Challenge Level

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

Rooted Via 10

Age 14 to 16 Short
Challenge Level

How many of the numbers shown are greater than 10?

Doubly Powerful

Age 14 to 16 Short
Challenge Level

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

Largest Expression

Age 14 to 16 Short
Challenge Level

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

Roots Near 9

Age 14 to 16 Short
Challenge Level

For how many integers 𝑛 is the difference between √𝑛 and 9 is less than 1?

Which Power?

Age 14 to 16 Short
Challenge Level

Which power of $16$ is equal to $64^6$?

The Power of $x$

Age 14 to 16 Short
Challenge Level

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

Self-power Squares

Age 14 to 16 Short
Challenge Level

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

Great Power

Age 14 to 16 Short
Challenge Level

Which is greater: $10^{250}$ or $6^{300}$?

Powerful 9

Age 14 to 16 Short
Challenge Level

What is the last digit of this calculation?

Power of 3

Age 14 to 16 Short
Challenge Level

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

Power of Five

Age 14 to 16 Short
Challenge Level

Powers with brackets, addition and multiplication

Know Your Powers

Age 14 to 16 Short
Challenge Level

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

Powered Up

Age 14 to 16 Short
Challenge Level

Can you work out the product of these indices?