Question 1

What is a square root?

Accepted Answer

The square root of n is a number x such that x × x = n. Written as √n. For example, √9 = 3 because 3 × 3 = 9. Every positive number has two square roots: positive and negative, but we usually take the principal (positive) root.

Question 2

What is a perfect square?

Accepted Answer

A perfect square is an integer that is the square of another integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots are whole numbers. Non-perfect squares (2, 3, 5, 7, ...) have irrational square roots.

Question 3

What is simplified radical form?

Accepted Answer

Simplified radical form rewrites √n by extracting perfect square factors. For example: √72 = √(36×2) = 6√2. This means the coefficient is 6 and the radicand is 2. A radical is fully simplified when no perfect square remains inside.

Question 4

What is the square root of 2?

Accepted Answer

√2 ≈ 1.41421356... It is an irrational number — the decimal never terminates or repeats. It was famously proven irrational by the ancient Greeks. It appears in the diagonal of a unit square (by Pythagoras' theorem).

Question 5

How do I calculate square root by hand?

Accepted Answer

Use the digit-by-digit method (long division for square roots) or estimate and refine. A quick estimate: if n is between a² and (a+1)², start with a + (n−a²)/(2a). For example, √50: between 7²=49 and 8²=64. Estimate: 7 + 1/14 ≈ 7.07. Refine by computing 7.07² ≈ 49.98. Close enough.

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