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Square Root of 102

The square root of 102 is expressed as √102 in the radical form and as (102)^½ or (102)^0.5 in the exponent form. The square root of 102 rounded up to 10 decimal places is 10.0995049384. It is the positive solution of the equation x² = 102.

Square Root of 102: 10.099504938362077
Square Root of 102 in exponential form: (102)^½ or (102)^0.5
Square Root of 102 in radical form: √102

Square Root of 102

1.	What is the Square Root of 102?
2.	How to find the Square Root of 102?
3.	Is the Square Root of 102 Irrational?
4.	FAQs

What is the Square Root of 102?

The square root of 102, (or root 102), is the number which when multiplied by itself gives the product as 102. Therefore, the square root of 102 = √102 = 10.099504938362077.

☛ Check: Square Root Calculator

How to Find Square Root of 102?

Square Root of 102 by Long Division Method

Value of √102 by Long Division Method

Explanation:

Forming pairs: 01 and 02
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 02, to the right of the remainder 0. The new dividend is now 2.
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 <= 2. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 2.
Divide 2 by 20 with the quotient as 0, giving the remainder = 2 - 20 × 0 = 2 - 0 = 2.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 2. The new dividend is now 200.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 0) such that 20Z × Z <= 200. Together they form a new divisor (200) for the new dividend (200).
Divide 200 by 200 with the quotient as 0, giving the remainder = 200 - 200 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 102.

Therefore, the square root of 102 by long division method is 10.0 approx.

Is Square Root of 102 Irrational?

The actual value of √102 is undetermined. The value of √102 up to 25 decimal places is 10.09950493836207795336339. Hence, the square root of 102 is an irrational number.

☛ Also Check:

Square Root of 2 - √2 = 1.41421
Square Root of 169 - √169 = 13
Square Root of 89 - √89 = 9.43398
Square Root of 35 - √35 = 5.91608
Square Root of 1000 - √1000 = 31.62278
Square Root of 72 - √72 = 8.48528
Square Root of 140 - √140 = 11.83216

Square Root of 102 Solved Examples

Example 1: Solve the equation x² − 102 = 0

Solution:

x² - 102 = 0 i.e. x² = 102
x = ±√102
Since the value of the square root of 102 is 10.100,
⇒ x = +√102 or -√102 = 10.100 or -10.100.
Example 2: If the area of a circle is 102π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 102π in²
⇒ r = ±√102 in
Since radius can't be negative,
⇒ r = √102
The square root of 102 is 10.100.
⇒ r = 10.100 in
Example 3: If the area of an equilateral triangle is 102√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 = 102√3 in²
⇒ a = ±√408 in
Since length can't be negative,
⇒ a = √408 = 2 √102
We know that the square root of 102 is 10.100.
⇒ a = 20.199 in

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FAQs on the Square Root of 102

What is the Value of the Square Root of 102?

The square root of 102 is 10.0995.

Why is the Square Root of 102 an Irrational Number?

Upon prime factorizing 102 i.e. 2¹ × 3¹ × 17¹, 2 is in odd power. Therefore, the square root of 102 is irrational.

Is the number 102 a Perfect Square?

The prime factorization of 102 = 2¹ × 3¹ × 17¹. Here, the prime factor 2 is not in the pair. Therefore, 102 is not a perfect square.

What is the Square Root of -102?

The square root of -102 is an imaginary number. It can be written as √-102 = √-1 × √102 = i √102 = 10.099i
where i = √-1 and it is called the imaginary unit.

What is the Value of 17 square root 102?

The square root of 102 is 10.100. Therefore, 17 √102 = 17 × 10.100 = 171.692.

What is the Square Root of 102 in Simplest Radical Form?

We need to express 102 as the product of its prime factors i.e. 102 = 2 × 3 × 17. Therefore, as visible, the radical form of the square root of 102 cannot be simplified further. Therefore, the simplest radical form of the square root of 102 can be written as √102

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