The price ofsquare root is created as (√) and also is one integral part of mathematics. As soon as you recognize the basics of finding the square root of a number, you have the right to solve any square root-related problem.

You are watching: Whats the square root of 13

Today, allow us discover the square root of 13, and also 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 root of 13:√13=3.60555128Square the 13: 132 = 169
1.What Is the Square root of 13?
2.IsSquare root of 13Rational or Irrational?
3.How to discover the Square source of 13?
4.FAQs top top Square source of 13

What Is the Square source of 13?

The square root of 13 is expressed as √13in the radical kind and as 13½in the exponent form.The square root of 13 rounded to 5 decimal places is ±3.60555.

Is the Square root of 13Rational orIrrational?

A number that cannot be expressed as a proportion of two integers is an irrational number. The decimal type of the irrational number is non-terminating (i.e., it never ever ends) and also non-recurring (i.e., the decimal component of the number never repeats a pattern). Now let united state look in ~ the square root of 13.

Is the square source of 13 rational or irrational?

√13= 3.60555128

Do friend think the decimal part stops after 3.60555128? No, that is never-ending and also you cannot watch a sample in the decimal part.

Square root of √13is an irrational number.

How to uncover the Square source of 13?

Square Roots can be calculate using miscellaneous methods:

By simple the radical that the number that room perfect squares.By long division method because that perfect and non-perfect squares

13 is a prime number and hence, the is not a perfect square. Therefore, the square source of 13 can only be calculated by the long division method.

Simplified Radical form of Square root of 13

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

√13 is in the lowest kind and cannot be streamlined further.We have expressed the square source of 13 in the radical form.

Square source of 13ByLong Division

Let us follow the steps to discover the square root of 13 by lengthy division.

Step 1: group the digits into pairs from appropriate to left by put a bar over it.Step 3: permit us location a decimal allude and bag of zeros after that to proceed our division.Now, multiply the quotient by 2 and the product i do not care the starting digit of our next divisor.Step 5: carry 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 of the brand-new divisor.Step 6: choose the biggest digit in the units location for the new divisor such that the product the the new divisor v the digit at ones ar is less than or equal to 400. We view that 721when multiply by 1, gives 721 which is better than 400. Therefore, we will take 720 ×0 = 0 which is much less than 400.Step 7: Add more pairs that zeros and repeat the procedure of detect the brand-new divisor and also product together done in step 2.Step 8: pick the largest digit in ~ the units location for the brand-new divisor such that the product the the new divisor through the number at ones ar is much less than or same to 40000. We see that 7205when multiply by 5, offers 36025which is less than 40000.


Thus, the square source of 13 obtained by long division is3.60555128.

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

Think Tank:

Can girlfriend think that a quadratic equation which has actually a root together √13?Since (-√13)2= 13, can we say that -√13is additionally 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 a question. The knew the 3.605 is thesquare root of 13 and wanted to understand if -3.605is also thesquare root of 13? deserve to you answerhis question?


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