Square Root Of 135 Simplified

The square root of 13 is given by √xiii in the radical form and as (13)^½ in exponential form. It is equal to iii.60555128. Since 3.60555128 is not a whole number but a fraction, therefore, 13 is not a perfect foursquare. The square root of thirteen is a value 10, such that X² = thirteen. Since 13 is a prime number, we cannot determine its foursquare root using the prime factorization method. But nosotros can apply here the long sectionalisation method to observe the square root of thirteen. Let us learn more in this article.

Square root of 13 = √13 (in radical form) Foursquare root of 13 = three.60555128 (in decimal or fraction) Foursquare root of 13 = xiii^1/2 (in exponential form)

What is the Square Root of thirteen?

The square root of 13 is the number that can be multiplied past itself to get the original number. Since 13 is not a perfect foursquare, therefore, its square root volition not result in a whole number. As we know, square root is the reverse method of squaring a number. Let u.s.a. say, 10 is a number that is squared to go the value equal to 13, such that 10ⁱⁱ = 13, then, √thirteen = x.

And so, the square root of xiii is approximately equal to 3.60555128 because the square of iii.60555128 is equal to 13.

√thirteen = 3.60555128

How to Detect the Foursquare Root of thirteen?

Basically, we have two methods to find the square root of any number. But in the example of 13, nosotros cannot apply the prime factorisation method to notice its square root.

Prime factorisation of 13 → 13

Thus, the simply prime number cistron that can dissever 13 is 13 itself. Hence, we cannot simplify it further. Let u.s. move to another method to find its square root.

Square Root of 13 By Long Sectionalization Method

Before proceeding to find the foursquare root, nosotros can write 13 every bit 13.000000. It doesn't make whatever difference in the number. Now we will use the long division method given as follows.

Step 1: Pair the digits of thirteen.000000 from left to correct such every bit 13.00 00 00
Pace 2: We demand to recollect of a number that tin can exist multiplied by itself to get a value less than or equal to the dividend xiii. Thus, 3 is the divisor such that, 3 x 3 = 9.
Step 3: Subtract 9 from xiii to get iv and take downwardly the next pair, 00, to brand the new dividend equal to 400
Step 4: Add 3 to the previous divisor. 3 + 3 = 6. Now, put a digit, say A, next to 6 such that 6A x A is less than or equal to 400. Hence, 66 ten half-dozen = 396
Footstep 5: Decrease 396 from 400 to go 4. Again, take down the next ii zeros, and so that 400 is the next dividend
Footstep 6: Add together half dozen to the previous divisor, i.e.,66 to become 72. Think of a digit that can be placed next to 72, such that 72B 10 B is less than or equal to 400 (dividend). Hence, 720 x 0 = 000
Pace 7: Subtract 000 from 400 to get 400 again. Once more, take down the next two zeros for the next sectionalisation
Step viii: Add 0 to the previous divisor such that, 720 + 0 = 720.
Pace 9: To split up 40000, we have to call back of a digit side by side to 720 such that 720C x C is less than or equal to 40000. Hence, 7205 10 v = 36025
Pace ten: Subtracting 36025 from 40000, we become 3975.
Pace xi: Now we have got the quotient value upwardly to three decimal places, i.e., 3.605. We can repeat the above steps to go a more accurate value.

Square root of 13

Therefore, the required square root of 13 is the caliber accomplished in the higher up division method, i.e., √13 = 3.605, approximately.

Square Root of 13 – Rational or Irrational

A rational number is a number that can be expressed every bit a ratio, such as P/Q, where Q is non equal to 0. Information technology is unremarkably a terminating or recurring decimal.
An irrational number cannot exist expressed as P/Q. It is a non-terminating and non-repeating decimal.
The square root of 13 is a non-terminating and non-repeating decimal. Hence, it is an irrational number.

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Solved Examples

Q.1: What is the value of √13 + √100?

Solution: As nosotros know;

√xiii = iii.606

√100 = ten

Therefore,

√thirteen + √100

⇒ 3.606 + x

⇒ 3.606 (up to three places of the decimal)

Q.two: What is the value of the square of root of xiii multiplied by 13?

Solution: Foursquare of root of 13 = (√13)^two

Since square root gets cancelled with foursquare, thus,

(√13)ⁱⁱ= 13

At present,

thirteen multiplied by xiii = xiii 10 13 = 169

Q.3: If the length of the side of a square is √13 units, and so what is the area of the square?

Solution: Given,

Length of side of square, south = √13 units

According to the formula,

Area of square = s²

A = (√thirteen)²

A = 13 sq.units.

Therefore, the area of a square is xiii sq. units.

Practice Questions

Find the value of y if, √thirteen – y² = 0.
What is the value of √-13?
Notice: √13 x 1/3.60555128 = ?

Ofttimes Asked Questions on Square Root of 13

What is the exact value of the foursquare root of 13?

The exact value of the square root of xiii is 3.60555128.

What is the square root of 13 in radical form?

The square root of 13 in radical form is expressed with a radical symbol, such equally √thirteen, where 13 is said to be radicand.

What is the simplest form of square root of 13?

The simplified grade of square root of 13 is √xiii. We cannot further simplify it.

What is the square of thirteen?

The square of xiii is 169.
13² = 13 ten thirteen = 169

How can we find the square root of xiii?

We can use long division to find the foursquare root of 13.

Is the foursquare root of 13 a fraction or a whole number?

The foursquare root of 13 is a fraction and not a whole number.

Is 13 a perfect square?

No, 13 is not a perfect square.

Is √thirteen a rational number?

No, √xiii = iii.60555128 is an irrational number.