Question 1

What does it mean to simplify a radical?

Accepted Answer

A square root is simplified when the number under the root has no perfect square factor bigger than 1. √72 is not simplified because 72 = 36 × 2; the simplified form is 6√2.

Question 2

How do I simplify a square root by hand?

Accepted Answer

Factor the number into primes, circle every pair of the same prime, and move one copy of each pair outside the root. Whatever is not in a pair stays inside. The calculator shows this exact process.

Question 3

Does it work for cube roots?

Accepted Answer

Yes. Switch the root to ∛ and it pulls out groups of three instead of pairs. ∛54 = ∛(27 × 2) = 3∛2.

Question 4

What happens with a negative number under a square root?

Accepted Answer

There is no real square root of a negative number, so the calculator writes the answer with i, the imaginary unit. √(-18) = 3√2 i. Cube roots of negatives are fine and come out negative.

Question 5

What if there is a number in front of the radical?

Accepted Answer

Enter it in the coefficient box. After simplifying the root, the calculator multiplies the coefficient by whatever came out of the radical: 3√50 = 3 × 5√2 = 15√2.