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Square Root of 270

The square root of 270 is expressed as √270 in the radical form and as (270)^½ or (270)^0.5 in the exponent form. The square root of 270 rounded up to 8 decimal places is 16.43167673. It is the positive solution of the equation x² = 270. We can express the square root of 270 in its lowest radical form as 3 √30.

Square Root of 270: 16.431676725154983
Square Root of 270 in exponential form: (270)^½ or (270)^0.5
Square Root of 270 in radical form: √270 or 3 √30

Square Root of 270

1.	What is the Square Root of 270?
2.	How to find the Square Root of 270?
3.	Is the Square Root of 270 Irrational?
4.	FAQs

What is the Square Root of 270?

The square root of 270, (or root 270), is the number which when multiplied by itself gives the product as 270. Therefore, the square root of 270 = √270 = 3 √30 = 16.431676725154983.

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How to Find Square Root of 270?

Square Root of 270 by Long Division Method

Value of √270 by Long Division Method

Explanation:

Forming pairs: 02 and 70
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 70, to the right of the remainder 1. The new dividend is now 170.
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 <= 170. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 170.
Divide 170 by 26 with the quotient as 6, giving the remainder = 170 - 26 × 6 = 170 - 156 = 14.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
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 <= 1400. Together they form a new divisor (324) for the new dividend (1400).
Divide 1400 by 324 with the quotient as 4, giving the remainder = 1400 - 324 × 4 = 1400 - 1296 = 104.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 270.

Therefore, the square root of 270 by long division method is 16.4 approx.

Is Square Root of 270 Irrational?

The actual value of √270 is undetermined. The value of √270 up to 25 decimal places is 16.43167672515498340370909. Hence, the square root of 270 is an irrational number.

☛ Also Check:

Square Root of 35 - √35 = 5.91608
Square Root of 140 - √140 = 11.83216
Square Root of 42 - √42 = 6.48074
Square Root of 96 - √96 = 9.79796
Square Root of 50 - √50 = 7.07107
Square Root of 76 - √76 = 8.71780
Square Root of 52 - √52 = 7.21110

Square Root of 270 Solved Examples

Example 1: Solve the equation x² − 270 = 0

Solution:

x² - 270 = 0 i.e. x² = 270
x = ±√270
Since the value of the square root of 270 is 16.432,
⇒ x = +√270 or -√270 = 16.432 or -16.432.
Example 2: If the surface area of a cube is 1620 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 = 1620 in²
⇒ a = ±√270 in
Since length can't be negative,
⇒ a = √270
We know that the square root of 270 is 16.432.
⇒ a = 16.432 in
Example 3: If the surface area of a sphere is 1080π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1080π in²
⇒ r = ±√270 in
Since radius can't be negative,
⇒ r = √270
The square root of 270 is 16.432.
⇒ r = 16.432 in

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FAQs on the Square Root of 270

What is the Value of the Square Root of 270?

The square root of 270 is 16.43167.

Why is the Square Root of 270 an Irrational Number?

Upon prime factorizing 270 i.e. 2¹ × 3³ × 5¹, 2 is in odd power. Therefore, the square root of 270 is irrational.

What is the Square Root of -270?

The square root of -270 is an imaginary number. It can be written as √-270 = √-1 × √270 = i √270 = 16.431i
where i = √-1 and it is called the imaginary unit.

What is the Value of 5 square root 270?

The square root of 270 is 16.432. Therefore, 5 √270 = 5 × 16.432 = 82.158.

What is the Square Root of 270 in Simplest Radical Form?

We need to express 270 as the product of its prime factors i.e. 270 = 2 × 3 × 3 × 3 × 5. Therefore, √270 = √2 × 3 × 3 × 3 × 5 = 3 √30. Thus, the square root of 270 in the lowest radical form is 3 √30.

Is the number 270 a Perfect Square?

The prime factorization of 270 = 2¹ × 3³ × 5¹. Here, the prime factor 2 is not in the pair. Therefore, 270 is not a perfect square.

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