The price ofsquare source is created as (√) and is one integral part of mathematics. When you recognize the basics of detect the square root of a number, you can solve any type of square root-related problem.

You are watching: What is square root of 13

Today, permit us find the square root of 13, and explore the answer to inquiries like, is the square source of 13 a rational number and the square source of 13 in radical form.

Square source of 13:√13=3.60555128Square that 13: 132 = 169
 1 What Is the Square root of 13? 2 IsSquare source of 13Rational or Irrational? 3 How to uncover the Square source of 13? 4 FAQs on Square source of 13

## What Is the Square source of 13?

The square source of 13 is expressed together √13in the radical kind and together 13½in the exponent form.The square root of 13 rounded come 5 decimal locations is ±3.60555.

## Is the Square root of 13Rational orIrrational?

A number that cannot it is in expressed together a proportion of 2 integers is one irrational number. The decimal type of the irrational number is non-terminating (i.e., it never ends) and non-recurring (i.e., the decimal component of the number never ever repeats a pattern). Now let us look in ~ the square root of 13.

Is the square source of 13 rational or irrational?

√13= 3.60555128

Do you think the decimal part stops after 3.60555128? No, the is never-ending and also you cannot check out a pattern in the decimal part.

Square source of √13is one irrational number.

## How to discover the Square source of 13?

Square Roots deserve to be calculated using assorted methods:

By simplifying the radical the the number that are perfect squares.By long department method because that perfect and non-perfect squares

13 is a prime number and also hence, it is no a perfect square. Therefore, the square root of 13 deserve to only it is in calculated by the long department method.

### Simplified Radical type of Square root of 13

To simplify the square source of 13, allow us very first express 13 together a product of its prime factors.

√13 is in the lowest kind and can not be simplified further.We have expressed the square source of 13 in the radical form.

### Square root of 13ByLong Division

Let united state follow the procedures to discover the square root of 13 by lengthy division.

Step 1: group the digits into pairs from right to left by placing a bar end it.Step 3: permit us ar a decimal point and pairs of zeros after the to continue our division.Now, multiply the quotient by 2 and the product becomes the starting digit of our next divisor.Step 5: bring down the next pair that zeros and multiply the quotient 36(ignore the decimal) through 2, i m sorry is 72, and the starting digit the the brand-new divisor.Step 6: pick the biggest digit in the units place for the brand-new divisor such that the product of the new divisor v the number at ones location is much less than or same to 400. We watch that 721when multiplied by 1, offers 721 which is greater than 400. Therefore, we will take 720 ×0 = 0 i m sorry is less than 400.Step 7: Add an ext pairs that zeros and repeat the procedure of finding the brand-new divisor and product together done in action 2.Step 8: choose the largest digit at the units ar for the new divisor such the the product that the brand-new divisor through the number at ones ar is less than or same to 40000. We view that 7205when multiplied by 5, gives 36025which is much less than 40000. Thus, the square root of 13 obtained by long department is3.60555128.

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Can you try and to express the square source of 17 in a comparable way? The price of √17should be 4.123

Think Tank:

Can you think the a quadratic equation which has a root as √13?Since (-√13)2= 13, deserve to we say the -√13is likewise a square source of 13?

Important Notes:

The square source of 13in the radical form, is expressed together √13.The square source of 13 is expressed together 13½in the exponent form.The actual roots that √13are ±3.605

Example 2

Thomas had actually a question. The knew that 3.605 is thesquare source of 13 and also wanted to understand if -3.605is likewise thesquare source of 13? can you answerhis question?

Solution

Let united state take an instance of a perfect square number and extend the same logic come answer his question.We understand that 2is a square root of 4because once 2is multiply to itself it provides 4.But what around -2?Let us multiply and also check.-2× -2= 4because (-) × (-) = (+)Therefore, -2is also a square source of 4.Going through the exact same logic,-3.605is likewise the square source of 13.