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.

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

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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

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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Value of √272 by Long Division Method

Explanation:

Forming pairs: 02 and 72Find a number Y (1) such that whose square is 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 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 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.


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.

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Example 1: Solve the equation x2 − 272 = 0

Solution:

x2 - 272 = 0 i.e. x2 = 272x = ±√272Since the value of the square root of 272 is 16.492,⇒ x = +√272 or -√272 = 16.492 or -16.492.


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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.

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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.