Primes, squares, cubes and roots

Prime means exactly two positive factors

A prime is a whole number greater than 1 with exactly two positive factors: 1 and itself. Seven is prime. Nine is not, because 3 is also a factor. One is not prime: it has only one positive factor. Two is the only even prime.

To decide whether 29 is prime, try possible divisors 2, 3, 4 and 5. None divides it exactly. A larger factor below 29 would pair with a factor smaller than square root of 29, so these checks suffice. This checks whether a number is prime. Expressing a composite number as a product of primes is a different task.

Squares, cubes and roots

A square uses two equal factors: 3² = 3 × 3 = 9. A cube uses three: 3³ = 27. Brackets distinguish (−3)² = 9 from −3² = −9. Check the intended negative base before entering it in a calculator.

The square root square root of 49 = 7 is the non-negative number whose square is 49. The cube root cube root of (-8) = -2, since (-2)³ = -8. For calculator work, enter brackets around a negative base and use the displayed sign to check the intended expression.

Roots do not undo every sign choice

A learner enters square root of 36 and gets 6. Does that mean x² = 36 has only one solution?