How do I simplify a square root by hand?
Pull out the largest perfect-square factor. √200 = √100 × √2 = 10√2. This is the exact form usually required in algebra classes.
Calculate square roots, cube roots, and nth roots of any number. See if a number is a perfect square with step-by-step breakdown.
√n = the value x where x² = n. √(ab) = √a × √b. Newton's method: x(next) = (x + n ÷ x) ÷ 2, repeated until stable.
√72 simplifies to √36 × √2 = 6√2 ≈ 8.485. Newton's method from a guess of 8 gives 8.5, then 8.4853 — accurate to four decimals in two steps.
Pull out the largest perfect-square factor. √200 = √100 × √2 = 10√2. This is the exact form usually required in algebra classes.
Not within real numbers. √−9 is expressed as 3i using imaginary numbers, which is why calculators return an error for negative inputs in real mode.
A square root asks what value squared gives n; a cube root asks what value cubed gives n. Unlike square roots, cube roots of negative numbers are real: ∛−27 = −3.