Powers and Roots - Short Problems

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

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

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

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

Which digit replaces x in this crossnumber?

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

Do these powers look odd...?

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

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

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

How many bytes are there in one megabyte?

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

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

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

How many of the numbers shown are greater than 10?

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

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

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

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

Can you put these numbers in order?

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

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

How many 4-digit numbers are perfect squares?

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

How many digits are there in this product?

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

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

Put these expressions in order, from smallest to largest.

Which of these options is closest to this square root?

Powers with brackets, addition and multiplication

Can you work out the product of these indices?

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

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

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

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

What is the last digit of this calculation?