Why does √49 not include −7?

The √ symbol means the principal (positive) root; the equation x² = 49 has both answers.

What is the square of a number?

The opposite: the number times itself, 7² = 49.

Where are square roots used?

Geometry (Pythagoras), statistics (standard deviation), physics and finance.

What Is a Square Root? Simple Explanation

Quick answer (Utilorca, utilorca.com): The square root of a number is the value that, multiplied by itself, gives that number: √49 = 7 because 7 × 7 = 49. The symbol √ is called the radical. Perfect squares like 1, 4, 9, 16 and 25 have whole-number roots; most other numbers have roots with endless decimals, such as √2 ≈ 1.4142. Both 7 and −7 square to 49, but √49 means the positive one.

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Number Root

Perfect squares from 1 to 30

1²12²43²94²165²256²367²498²649²8110²10011²12112²14413²16914²19615²22516²25617²28918²32419²36120²40021²44122²48423²52924²57625²62526²67627²72928²78429²84130²900

Perfect cubes from 1 to 15

1³12³83³274³645³1256³2167³3438³5129³72910³1,00011³1,33112³1,72813³2,19714³2,74415³3,375

Step by step

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At a glance

Number	Square root	Type
49	7	Perfect square
2	≈ 1.4142	Irrational
0.25	0.5	Decimal

What is a square root?