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What Is the Square Roots?(With Examples)

A square root of a number is a value that, when multiplied by itself, gives the original number. The square root of 16 is 4 because 4 × 4 = 16. The symbol √ is called the radical sign.

Grade 8Key Stage 3-4Årskurs 8-9Klasse 8-9

📖Definition

A square root of a number is a value that, when multiplied by itself, gives the original number. The square root of 16 is 4 because 4 × 4 = 16. The symbol √ is called the radical sign.

📐Formula

√a = b means b² = a

If √a = b, then b × b = a. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots: one positive and one negative, but √ typically refers to the positive root.

📝Step-by-Step Guide

Identify Perfect Squares

Check if the number is a perfect square (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...).

Simplify Non-Perfect Squares

Factor out perfect squares from under the radical.

√72 = √(36 × 2) = √36 × √2 = 6√2

Estimate Square Roots

For non-perfect squares, find which two perfect squares the number falls between.

√50 is between √49 (7) and √64 (8), closer to 7

Multiply and Divide Radicals

Use the rules: √a × √b = √(ab) and √a ÷ √b = √(a/b).

⚠️Common Mistakes to Avoid

Thinking √(a + b) = √a + √b (this is wrong!)
Forgetting that √a² = |a| (absolute value)
Not fully simplifying radicals
Confusing square roots with dividing by 2
Missing the negative square root when solving equations

✏️Practice Problems

Easy

Calculate √81

Answer: 9

Medium

Simplify √48

Answer: 4√3

Hard

Simplify √75 + √27

Answer: 8√3

Printable Square Roots practice

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Worked Examples

Square Root Examplemedium

Exponents Pythagorean Theorem Radicals Irrational Numbers

Curriculum Alignment

CommonCore (8.EE.A.2)KS3KMK

Classroom assessment context

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