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Square Root of 220

The square root of 220 is expressed as √220 in the radical form and as (220)^½ or (220)^0.5 in the exponent form. The square root of 220 rounded up to 5 decimal places is 14.83240. It is the positive solution of the equation x² = 220. We can express the square root of 220 in its lowest radical form as 2 √55.

Square Root of 220: 14.832396974191326
Square Root of 220 in exponential form: (220)^½ or (220)^0.5
Square Root of 220 in radical form: √220 or 2 √55

Square Root of 220

1.	What is the Square Root of 220?
2.	How to find the Square Root of 220?
3.	Is the Square Root of 220 Irrational?
4.	FAQs

What is the Square Root of 220?

The square root of 220, (or root 220), is the number which when multiplied by itself gives the product as 220. Therefore, the square root of 220 = √220 = 2 √55 = 14.832396974191326.

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How to Find Square Root of 220?

Square Root of 220 by Long Division Method

Value of √220 by Long Division Method

Explanation:

Forming pairs: 02 and 20
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 20, to the right of the remainder 1. The new dividend is now 120.
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 4) such that 2Z × Z <= 120. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 120.
Divide 120 by 24 with the quotient as 4, giving the remainder = 120 - 24 × 4 = 120 - 96 = 24.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 8) such that 28Z × Z <= 2400. Together they form a new divisor (288) for the new dividend (2400).
Divide 2400 by 288 with the quotient as 8, giving the remainder = 2400 - 288 × 8 = 2400 - 2304 = 96.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 220.

Therefore, the square root of 220 by long division method is 14.8 approx.

Is Square Root of 220 Irrational?

The actual value of √220 is undetermined. The value of √220 up to 25 decimal places is 14.83239697419132589742279. Hence, the square root of 220 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 17 - √17 = 4.12311
Square Root of 13 - √13 = 3.60555
Square Root of 289 - √289 = 17
Square Root of 12 - √12 = 3.46410
Square Root of 22 - √22 = 4.69042
Square Root of 1521 - √1521 = 39

Square Root of 220 Solved Examples

Example 1: Solve the equation x² − 220 = 0

Solution:

x² - 220 = 0 i.e. x² = 220
x = ±√220
Since the value of the square root of 220 is 14.832,
⇒ x = +√220 or -√220 = 14.832 or -14.832.
Example 2: If the surface area of a cube is 1320 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 = 1320 in²
⇒ a = ±√220 in
Since length can't be negative,
⇒ a = √220
We know that the square root of 220 is 14.832.
⇒ a = 14.832 in
Example 3: If the area of an equilateral triangle is 220√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 = 220√3 in²
⇒ a = ±√880 in
Since length can't be negative,
⇒ a = √880 = 2 √220
We know that the square root of 220 is 14.832.
⇒ a = 29.665 in

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FAQs on the Square Root of 220

What is the Value of the Square Root of 220?

The square root of 220 is 14.83239.

Why is the Square Root of 220 an Irrational Number?

Upon prime factorizing 220 i.e. 2² × 5¹ × 11¹, 5 is in odd power. Therefore, the square root of 220 is irrational.

What is the Square of the Square Root of 220?

The square of the square root of 220 is the number 220 itself i.e. (√220)² = (220)^2/2 = 220.

What is the Value of 18 square root 220?

The square root of 220 is 14.832. Therefore, 18 √220 = 18 × 14.832 = 266.983.

Is the number 220 a Perfect Square?

The prime factorization of 220 = 2² × 5¹ × 11¹. Here, the prime factor 5 is not in the pair. Therefore, 220 is not a perfect square.

If the Square Root of 220 is 14.832. Find the Value of the Square Root of 2.2.

Let us represent √2.2 in p/q form i.e. √(220/100) = 2.2/10 = 1.483. Hence, the value of √2.2 = 1.483

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