Powers and Roots quiz
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Which number equals $0.5^2$?
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More questions about Powers and Roots
These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.
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What is $10^{100}$ called?
Answer: Googol
Why: A googolplex is 10 to the power of a googol, a 1 followed by a googol zeros, which is physically impossible to write out.
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About how many years is $10^9$ seconds?
Answer: About 32 years
Why: With 31,557,600 seconds in a year, close to $\pi \times 10^7$, $10^9$ seconds comes to about 31.7 years.
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Which positive number's square equals itself plus 1?
Answer: Golden ratio
Why: Dividing $\varphi^2 = \varphi + 1$ by $\varphi$ gives $\frac{1}{\varphi} = \varphi - 1$, so 1.618 and its reciprocal 0.618 share their decimals.
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What is half of $2^{10}$?
Answer: $2^9$
Why: Halving removes just one factor of 2, so half of 1,024 is $2^9 = 512$, while $2^5$ is only 32.
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How many squares of all sizes does a chessboard contain?
Answer: 204
Why: Counting every size gives $8^2 + 7^2 + \dots + 1^2$: 64 single squares, 49 two-by-two squares, down to one board-sized square.
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What is the smallest sum of two positive cubes in two different ways?
Answer: 1,729
Why: 1,729 is $1^3 + 12^3$ and also $9^3 + 10^3$, just one more than the cube 1,728.
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