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Square Root of 103

The square root of 103 is expressed as √103 in the radical form and as (103)^½ or (103)^0.5 in the exponent form. The square root of 103 rounded up to 9 decimal places is 10.148891565. It is the positive solution of the equation x² = 103.

Square Root of 103: 10.14889156509222
Square Root of 103 in exponential form: (103)^½ or (103)^0.5
Square Root of 103 in radical form: √103

Square Root of 103

1.	What is the Square Root of 103?
2.	How to find the Square Root of 103?
3.	Is the Square Root of 103 Irrational?
4.	FAQs

What is the Square Root of 103?

The square root of 103, (or root 103), is the number which when multiplied by itself gives the product as 103. Therefore, the square root of 103 = √103 = 10.14889156509222.

☛ Check: Square Root Calculator

How to Find Square Root of 103?

Square Root of 103 by Long Division Method

Value of √103 by Long Division Method

Explanation:

Forming pairs: 01 and 03
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 03, to the right of the remainder 0. The new dividend is now 3.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 0) such that 2Z × Z <= 3. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 3.
Divide 3 by 20 with the quotient as 0, giving the remainder = 3 - 20 × 0 = 3 - 0 = 3.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 3. The new dividend is now 300.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 1) such that 20Z × Z <= 300. Together they form a new divisor (201) for the new dividend (300).
Divide 300 by 201 with the quotient as 1, giving the remainder = 300 - 201 × 1 = 300 - 201 = 99.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 103.

Therefore, the square root of 103 by long division method is 10.1 approx.

Is Square Root of 103 Irrational?

The actual value of √103 is undetermined. The value of √103 up to 25 decimal places is 10.14889156509221946864852. Hence, the square root of 103 is an irrational number.

☛ Also Check:

Square Root of 90 - √90 = 9.48683
Square Root of 13 - √13 = 3.60555
Square Root of 52 - √52 = 7.21110
Square Root of 225 - √225 = 15
Square Root of 76 - √76 = 8.71780
Square Root of 784 - √784 = 28
Square Root of 41 - √41 = 6.40312

Square Root of 103 Solved Examples

Example 1: Solve the equation x² − 103 = 0

Solution:

x² - 103 = 0 i.e. x² = 103
x = ±√103
Since the value of the square root of 103 is 10.149,
⇒ x = +√103 or -√103 = 10.149 or -10.149.
Example 2: If the area of an equilateral triangle is 103√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 103√3 in²
⇒ a = ±√412 in
Since length can't be negative,
⇒ a = √412 = 2 √103
We know that the square root of 103 is 10.149.
⇒ a = 20.298 in
Example 3: If the surface area of a sphere is 412π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 412π in²
⇒ r = ±√103 in
Since radius can't be negative,
⇒ r = √103
The square root of 103 is 10.149.
⇒ r = 10.149 in

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FAQs on the Square Root of 103

What is the Value of the Square Root of 103?

The square root of 103 is 10.14889.

Why is the Square Root of 103 an Irrational Number?

The number 103 is prime. This implies that the number 103 is pairless and is not in the power of 2. Therefore, the square root of 103 is irrational.

What is the Square Root of -103?

The square root of -103 is an imaginary number. It can be written as √-103 = √-1 × √103 = i √103 = 10.148i
where i = √-1 and it is called the imaginary unit.

What is the Value of 1 square root 103?

The square root of 103 is 10.149. Therefore, 1 √103 = 1 × 10.149 = 10.149.

If the Square Root of 103 is 10.149. Find the Value of the Square Root of 1.03.

Let us represent √1.03 in p/q form i.e. √(103/100) = 1.03/10 = 1.015. Hence, the value of √1.03 = 1.015

What is the Square Root of 103 in Simplest Radical Form?

The number 103 is a prime number. This implies that the number 103 is pairless and is not in the power of 2. Therefore, the radical form of square root of 103 cannot be simplified further.

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