The **square root** is a number that once multiplied by itself will equal the initial number. For instance, **7** is the square root of **49**, since **7** times **7** equals **49**. This is an amazing idea and also can be challenging to understand.

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The symbol **√** is referred to as the radical authorize and represents the square root procedure. Many kind of numbers have actually an integer square root. However, there are many type of even more numbers via irrational square roots.

The result of taking the square root of a number consists of both a positive and also negative number. However, when you take the square root of an unfavorable number, the result is referred to as an imaginary number.

Questions you might have include:

What is the radical sign?How perform you discover the square root of a number?What are imaginary numbers?This lesboy will answer those questions.

## Radical sign

The symbol **√** is called the radical authorize and also represents the square root operation. Therefore, **√49** implies the square root of **49**, and also **√z** indicates the square root of **z**.

You deserve to also designate a square root by the **1/2** exponent, such as **491/2** or **z1/2**, however typically the radical authorize is supplied.

## Finding the square root

The outcome of taking the square root of a number is composed of both a positive and also negative number. Thus **√49 = ±7** or **+7** and **−7**. This is bereason both **(+7)*(+7)** and **(−7)*(−7)** amounts to **49**.

Likewise **√x2 = ±x**

Many type of numbers have actually an integer square root. Common integer square roots are:

√1 = ±1 | √36 = ±6 |

√4 = ±2 | √49 = ±7 |

√9 = ±3 | √64 = ± 8 |

√16 = ±4 | √81 = ±9 |

√25 = ±5 | √100 = ±10 |

However before, tright here are many more square roots that are not integers, such as **√2**, **√3**, and **√5**. They are regularly repeating numbers:

**√2 = ±1.414213562373095...** or roughly **±1.414**

**√5 = ±2.23606797749979...** or approximately **±2.236**

You have the right to memorize many of the numbers that have actually an integer square root. Otherwise, you can usage a calculator to find the square root or even usage Newton"s Square Root Approximation approach. There are additionally online square root calculators.

## Imaginary numbers

Keep in mind that as soon as you take the square root of an unfavorable number, the result is referred to as an **imaginary** **number**. The square root of **−1** or **√(−1)** is designated as the imaginary number **i**. In various other words, it is not a actual number in our numeric system.

When you take the square root of an unfavorable number such as **√(−49)** you acquire a response of **±7i**. The reason is that **−49 = −1*49**.

## Summary

The square root of a number is another number that once multiplied by itself will certainly equal the initial number. The symbol **√** is referred to as the radical sign and represents the square root operation. Many numbers have actually an integer square root. The result of taking the square root of a number is composed of both a positive and also negative number. When you take the square root of a negative number, the outcome is called an imaginary number.

Be radical in your approach

## Reresources and also references

**Ron Kurtus" Credentials**

### Websites

**Roots and Radicals** - Purplemath.com

**Square Root Calculator** - Math.com

**Square Root** - Wikipedia

**Algebra Resources**

### Books

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**Top-rated books on Algebra**

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