How Square Roots Work
The square root of a number x is a value y such that y² = x. For example, √144 = 12 because 12² = 144. The symbol √ is called a radical sign.
√x = x1/2 | ∛x = x1/3 | ⁿ√x = x1/n
Simplifying Square Roots
To simplify √72: find the largest perfect square factor. 72 = 36 × 2, so √72 = √36 × √2 = 6√2.
Properties of Square Roots
- √(a × b) = √a × √b
- √(a / b) = √a / √b
- (√a)² = a
- √a² = |a| (absolute value)
- Square root of a negative number is imaginary: √(-1) = i
Frequently Asked Questions
What is a perfect square? A perfect square is an integer that is the square of another integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Can you take the square root of a negative number? Not in real numbers. The square root of a negative number involves imaginary numbers (i = √−1). For example, √−9 = 3i.
How do I estimate square roots? Find the two perfect squares the number falls between. √50 is between √49 (7) and √64 (8), closer to 7. Actual: 7.07.