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Square Root of 272

The square root of 272 is expressed as √272 in the radical form and as (272)^½ or (272)^0.5 in the exponent form. The square root of 272 rounded up to 5 decimal places is 16.49242. It is the positive solution of the equation x² = 272. We can express the square root of 272 in its lowest radical form as 4 √17.

Square Root of 272: 16.492422502470642
Square Root of 272 in exponential form: (272)^½ or (272)^0.5
Square Root of 272 in radical form: √272 or 4 √17

Square Root of 272

1.	What is the Square Root of 272?
2.	How to find the Square Root of 272?
3.	Is the Square Root of 272 Irrational?
4.	FAQs

What is the Square Root of 272?

The square root of 272, (or root 272), is the number which when multiplied by itself gives the product as 272. Therefore, the square root of 272 = √272 = 4 √17 = 16.492422502470642.

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How to Find Square Root of 272?

Square Root of 272 by Long Division Method

Value of √272 by Long Division Method

Explanation:

Forming pairs: 02 and 72
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 72, to the right of the remainder 1. The new dividend is now 172.
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 6) such that 2Z × Z <= 172. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 172.
Divide 172 by 26 with the quotient as 6, giving the remainder = 172 - 26 × 6 = 172 - 156 = 16.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 16. The new dividend is now 1600.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 4) such that 32Z × Z <= 1600. Together they form a new divisor (324) for the new dividend (1600).
Divide 1600 by 324 with the quotient as 4, giving the remainder = 1600 - 324 × 4 = 1600 - 1296 = 304.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 272.

Therefore, the square root of 272 by long division method is 16.4 approx.

Is Square Root of 272 Irrational?

The actual value of √272 is undetermined. The value of √272 up to 25 decimal places is 16.49242250247064219928564. Hence, the square root of 272 is an irrational number.

☛ Also Check:

Square Root of 2 - √2 = 1.41421
Square Root of 25 - √25 = 5
Square Root of 65 - √65 = 8.06226
Square Root of 1521 - √1521 = 39
Square Root of 16 - √16 = 4
Square Root of 75 - √75 = 8.66025
Square Root of 324 - √324 = 18

Square Root of 272 Solved Examples

Example 1: Solve the equation x² − 272 = 0

Solution:

x² - 272 = 0 i.e. x² = 272
x = ±√272
Since the value of the square root of 272 is 16.492,
⇒ x = +√272 or -√272 = 16.492 or -16.492.
Example 2: If the area of an equilateral triangle is 272√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 = 272√3 in²
⇒ a = ±√1088 in
Since length can't be negative,
⇒ a = √1088 = 2 √272
We know that the square root of 272 is 16.492.
⇒ a = 32.985 in
Example 3: If the surface area of a cube is 1632 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 = 1632 in²
⇒ a = ±√272 in
Since length can't be negative,
⇒ a = √272
We know that the square root of 272 is 16.492.
⇒ a = 16.492 in

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FAQs on the Square Root of 272

What is the Value of the Square Root of 272?

The square root of 272 is 16.49242.

Why is the Square Root of 272 an Irrational Number?

Upon prime factorizing 272 i.e. 2⁴ × 17¹, 17 is in odd power. Therefore, the square root of 272 is irrational.

Is the number 272 a Perfect Square?

The prime factorization of 272 = 2⁴ × 17¹. Here, the prime factor 17 is not in the pair. Therefore, 272 is not a perfect square.

What is the Value of 10 square root 272?

The square root of 272 is 16.492. Therefore, 10 √272 = 10 × 16.492 = 164.924.

What is the Square Root of 272 in Simplest Radical Form?

We need to express 272 as the product of its prime factors i.e. 272 = 2 × 2 × 2 × 2 × 17. Therefore, √272 = √2 × 2 × 2 × 2 × 17 = 4 √17. Thus, the square root of 272 in the lowest radical form is 4 √17.

What is the Square of the Square Root of 272?

The square of the square root of 272 is the number 272 itself i.e. (√272)² = (272)^2/2 = 272.

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