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Square Root of 280

The square root of 280 is expressed as √280 in the radical form and as (280)^½ or (280)^0.5 in the exponent form. The square root of 280 rounded up to 8 decimal places is 16.73320053. It is the positive solution of the equation x² = 280. We can express the square root of 280 in its lowest radical form as 2 √70.

Square Root of 280: 16.73320053068151
Square Root of 280 in exponential form: (280)^½ or (280)^0.5
Square Root of 280 in radical form: √280 or 2 √70

Square Root of 280

1.	What is the Square Root of 280?
2.	How to find the Square Root of 280?
3.	Is the Square Root of 280 Irrational?
4.	FAQs

What is the Square Root of 280?

The square root of 280, (or root 280), is the number which when multiplied by itself gives the product as 280. Therefore, the square root of 280 = √280 = 2 √70 = 16.73320053068151.

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How to Find Square Root of 280?

Square Root of 280 by Long Division Method

Value of √280 by Long Division Method

Explanation:

Forming pairs: 02 and 80
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 80, to the right of the remainder 1. The new dividend is now 180.
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 <= 180. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 180.
Divide 180 by 26 with the quotient as 6, giving the remainder = 180 - 26 × 6 = 180 - 156 = 24.
Now, let's find the decimal places after the quotient 16.
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. 6 + 26 = 32. To the right of 32, find a digit Z (which is 7) such that 32Z × Z <= 2400. Together they form a new divisor (327) for the new dividend (2400).
Divide 2400 by 327 with the quotient as 7, giving the remainder = 2400 - 327 × 7 = 2400 - 2289 = 111.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 280.

Therefore, the square root of 280 by long division method is 16.7 approximately.

Is Square Root of 280 Irrational?

The actual value of √280 is undetermined. The value of √280 up to 25 decimal places is 16.73320053068151095956344. Hence, the square root of 280 is an irrational number.

☛ Also Check:

Square Root of 35 - √35 = 5.91608
Square Root of 23 - √23 = 4.79583
Square Root of 61 - √61 = 7.81025
Square Root of 1681 - √1681 = 41
Square Root of 30 - √30 = 5.47723
Square Root of 10 - √10 = 3.16228
Square Root of 16 - √16 = 4

Square Root of 280 Solved Examples

Example 1: Solve the equation x² − 280 = 0

Solution:

x² - 280 = 0 i.e. x² = 280
x = ±√280
Since the value of the square root of 280 is 16.733,
⇒ x = +√280 or -√280 = 16.733 or -16.733.
Example 2: If the area of a square is 280 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 280 in²
⇒ a = ±√280 in
Since length can't be negative,
⇒ a = √280 = 16.733 in
Example 3: If the surface area of a cube is 1680 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 = 1680 in²
⇒ a = ±√280 in
Since length can't be negative,
⇒ a = √280
We know that the square root of 280 is 16.733.
⇒ a = 16.733 in

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FAQs on the Square Root of 280

What is the Value of the Square Root of 280?

The square root of 280 is 16.7332.

Why is the Square Root of 280 an Irrational Number?

Upon prime factorizing 280 i.e. 2³ × 5¹ × 7¹, 2 is in odd power. Therefore, the square root of 280 is irrational.

If the Square Root of 280 is 16.733. Find the Value of the Square Root of 2.8.

Let us represent √2.8 in p/q form i.e. √(280/100) = 2.8/10 = 1.673. Hence, the value of √2.8 = 1.673

What is the Square of the Square Root of 280?

The square of the square root of 280 is the number 280 itself i.e. (√280)² = (280)^2/2 = 280.

What is the Value of 12 square root 280?

The square root of 280 is 16.733. Therefore, 12 √280 = 12 × 16.733 = 200.798.

What is the Square Root of 280 in Simplest Radical Form?

We need to express 280 as the product of its prime factors i.e. 280 = 2 × 2 × 2 × 5 × 7. Therefore, √280 = √2 × 2 × 2 × 5 × 7 = 2 √70. Thus, the square root of 280 in the lowest radical form is 2 √70.

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