Square Root Of 169 Simplified

The square root of thirteen is given by √13 in the radical class and as (13)^½ in exponential form. Information technology is equal to three.60555128. Since iii.60555128 is not a whole number but a fraction, therefore, thirteen is not a perfect square. The foursquare root of 13 is a value Ten, such that X^two = xiii. Since 13 is a prime number, we cannot decide its foursquare root using the prime factorization method. But we can use here the long sectionalization method to find the square root of thirteen. Permit us learn more in this article.

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

What is the Foursquare Root of xiii?

The square root of 13 is the number that can be multiplied by itself to get the original number. Since 13 is not a perfect square, therefore, its square root will non outcome in a whole number. As we know, square root is the reverse method of squaring a number. Allow us say, ten is a number that is squared to get the value equal to 13, such that x^two = 13, and then, √xiii = x.

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

√13 = 3.60555128

How to Notice the Square Root of xiii?

Basically, we have two methods to observe the square root of whatsoever number. Merely in the example of thirteen, we cannot use the prime factorisation method to observe its square root.

Prime factorisation of xiii → xiii

Thus, the but prime factor that can divide thirteen is xiii itself. Hence, we cannot simplify information technology farther. Let us motility to some other method to detect its square root.

Foursquare Root of 13 Past Long Segmentation Method

Before proceeding to find the square root, we can write 13 every bit 13.000000. Information technology doesn't make any divergence in the number. Now we will use the long division method given every bit follows.

Step 1: Pair the digits of 13.000000 from left to right such equally 13.00 00 00
Step two: Nosotros need to remember of a number that can exist multiplied by itself to get a value less than or equal to the dividend thirteen. Thus, three is the divisor such that, 3 x iii = 9.
Step 3: Subtract nine from 13 to become 4 and have down the adjacent pair, 00, to make the new dividend equal to 400
Footstep 4: Add 3 to the previous divisor. iii + 3 = half-dozen. Now, put a digit, say A, next to 6 such that 6A 10 A is less than or equal to 400. Hence, 66 ten 6 = 396
Step five: Subtract 396 from 400 to get 4. Again, take down the next 2 zeros, so that 400 is the next dividend
Pace 6: Add together vi to the previous divisor, i.e.,66 to get 72. Call back of a digit that can be placed next to 72, such that 72B x B is less than or equal to 400 (dividend). Hence, 720 x 0 = 000
Footstep 7: Subtract 000 from 400 to go 400 once again. Again, have downward the next two zeros for the next division
Step 8: Add 0 to the previous divisor such that, 720 + 0 = 720.
Step 9: To divide 40000, we have to think of a digit side by side to 720 such that 720C 10 C is less than or equal to 40000. Hence, 7205 10 5 = 36025
Step 10: Subtracting 36025 from 40000, we get 3975.
Step 11: Now we have got the quotient value up to three decimal places, i.due east., 3.605. We can repeat the above steps to become a more authentic value.

Square root of 13

Therefore, the required square root of 13 is the quotient accomplished in the above division method, i.due east., √thirteen = 3.605, approximately.

Foursquare Root of 13 – Rational or Irrational

A rational number is a number that can be expressed as a ratio, such as P/Q, where Q is non equal to 0. It is normally a terminating or recurring decimal.
An irrational number cannot be expressed as P/Q. It is a non-terminating and not-repeating decimal.
The square root of 13 is a not-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: Equally we know;

√13 = 3.606

√100 = x

Therefore,

√13 + √100

⇒ iii.606 + x

⇒ iii.606 (upwardly to three places of the decimal)

Q.2: What is the value of the square of root of 13 multiplied by 13?

Solution: Foursquare of root of 13 = (√13)ⁱⁱ

Since square root gets cancelled with square, thus,

(√13)ⁱⁱ= 13

Now,

thirteen multiplied past 13 = 13 10 xiii = 169

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

Solution: Given,

Length of side of square, s = √xiii units

According to the formula,

Expanse of square = s²

A = (√13)²

A = 13 sq.units.

Therefore, the expanse of a square is 13 sq. units.

Practice Questions

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

Frequently Asked Questions on Square Root of 13

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

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

What is the square root of thirteen in radical form?

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

What is the simplest form of square root of 13?

The simplified class of square root of 13 is √13. We cannot further simplify information technology.

What is the square of 13?

The square of 13 is 169.
13^two = 13 x xiii = 169

How can we discover the foursquare root of 13?

We can use long division to detect the square root of xiii.

Is the square root of thirteen a fraction or a whole number?

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

Is 13 a perfect foursquare?

No, xiii is not a perfect square.

Is √thirteen a rational number?

No, √13 = three.60555128 is an irrational number.