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Square Root of 242

The square root of 242 is expressed as √242 in the radical form and as (242)^½ or (242)^0.5 in the exponent form. The square root of 242 rounded up to 10 decimal places is 15.5563491861. It is the positive solution of the equation x² = 242. We can express the square root of 242 in its lowest radical form as 11 √2.

Square Root of 242: 15.556349186104045
Square Root of 242 in exponential form: (242)^½ or (242)^0.5
Square Root of 242 in radical form: √242 or 11 √2

Square Root of 242

1.	What is the Square Root of 242?
2.	How to find the Square Root of 242?
3.	Is the Square Root of 242 Irrational?
4.	FAQs

What is the Square Root of 242?

The square root of 242, (or root 242), is the number which when multiplied by itself gives the product as 242. Therefore, the square root of 242 = √242 = 11 √2 = 15.556349186104045.

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How to Find Square Root of 242?

Square Root of 242 by Long Division Method

Value of √242 by Long Division Method

Explanation:

Forming pairs: 02 and 42
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 42, to the right of the remainder 1. The new dividend is now 142.
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 5) such that 2Z × Z <= 142. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 142.
Divide 142 by 25 with the quotient as 5, giving the remainder = 142 - 25 × 5 = 142 - 125 = 17.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 17. The new dividend is now 1700.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 5) such that 30Z × Z <= 1700. Together they form a new divisor (305) for the new dividend (1700).
Divide 1700 by 305 with the quotient as 5, giving the remainder = 1700 - 305 × 5 = 1700 - 1525 = 175.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 242.

Therefore, the square root of 242 by long division method is 15.5 approx.

Is Square Root of 242 Irrational?

The actual value of √242 is undetermined. The value of √242 up to 25 decimal places is 15.55634918610404553681858. Hence, the square root of 242 is an irrational number.

☛ Also Check:

Square Root of 625 - √625 = 25
Square Root of 50 - √50 = 7.07107
Square Root of 21 - √21 = 4.58258
Square Root of 40 - √40 = 6.32456
Square Root of 29 - √29 = 5.38516
Square Root of 106 - √106 = 10.29563
Square Root of 14 - √14 = 3.74166

Square Root of 242 Solved Examples

Example 1: Solve the equation x² − 242 = 0

Solution:

x² - 242 = 0 i.e. x² = 242
x = ±√242
Since the value of the square root of 242 is 15.556,
⇒ x = +√242 or -√242 = 15.556 or -15.556.
Example 2: If the area of a circle is 242π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 242π in²
⇒ r = ±√242 in
Since radius can't be negative,
⇒ r = √242
The square root of 242 is 15.556.
⇒ r = 15.556 in
Example 3: If the surface area of a cube is 1452 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1452 in²
⇒ a = ±√242 in
Since length can't be negative,
⇒ a = √242
We know that the square root of 242 is 15.556.
⇒ a = 15.556 in

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FAQs on the Square Root of 242

What is the Value of the Square Root of 242?

The square root of 242 is 15.55634.

Why is the Square Root of 242 an Irrational Number?

Upon prime factorizing 242 i.e. 2¹ × 11², 2 is in odd power. Therefore, the square root of 242 is irrational.

What is the Square Root of -242?

The square root of -242 is an imaginary number. It can be written as √-242 = √-1 × √242 = i √242 = 15.556i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 242 is 15.556. Find the Value of the Square Root of 2.42.

Let us represent √2.42 in p/q form i.e. √(242/100) = 2.42/10 = 1.556. Hence, the value of √2.42 = 1.556

What is the Value of 6 square root 242?

The square root of 242 is 15.556. Therefore, 6 √242 = 6 × 15.556 = 93.338.

Is the number 242 a Perfect Square?

The prime factorization of 242 = 2¹ × 11². Here, the prime factor 2 is not in the pair. Therefore, 242 is not a perfect square.

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