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Square Root of 980

The square root of 980 is expressed as √980 in the radical form and as (980)^½ or (980)^0.5 in the exponent form. The square root of 980 rounded up to 6 decimal places is 31.304952. It is the positive solution of the equation x² = 980. We can express the square root of 980 in its lowest radical form as 14 √5.

Square Root of 980: 31.304951684997057
Square Root of 980 in exponential form: (980)^½ or (980)^0.5
Square Root of 980 in radical form: √980 or 14 √5

Square Root of 980

1.	What is the Square Root of 980?
2.	How to find the Square Root of 980?
3.	Is the Square Root of 980 Irrational?
4.	FAQs

What is the Square Root of 980?

The square root of 980, (or root 980), is the number which when multiplied by itself gives the product as 980. Therefore, the square root of 980 = √980 = 14 √5 = 31.304951684997057.

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How to Find Square Root of 980?

Square Root of 980 by Long Division Method

Value of √980 by Long Division Method

Explanation:

Forming pairs: 09 and 80
Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
Bring down the next pair 80, to the right of the remainder 0. The new dividend is now 80.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 1) such that 6Z × Z <= 80. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 80.
Divide 80 by 61 with the quotient as 1, giving the remainder = 80 - 61 × 1 = 80 - 61 = 19.
Now, let's find the decimal places after the quotient 31.
Bring down 00 to the right of this remainder 19. The new dividend is now 1900.
Add the last digit of quotient to divisor i.e. 1 + 61 = 62. To the right of 62, find a digit Z (which is 3) such that 62Z × Z <= 1900. Together they form a new divisor (623) for the new dividend (1900).
Divide 1900 by 623 with the quotient as 3, giving the remainder = 1900 - 623 × 3 = 1900 - 1869 = 31.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 980.

Therefore, the square root of 980 by long division method is 31.3 approx.

Is Square Root of 980 Irrational?

The actual value of √980 is undetermined. The value of √980 up to 25 decimal places is 31.30495168499705574972843. Hence, the square root of 980 is an irrational number.

☛ Also Check:

Square Root of 48 - √48 = 6.92820
Square Root of 45 - √45 = 6.70820
Square Root of 76 - √76 = 8.71780
Square Root of 729 - √729 = 27
Square Root of 90 - √90 = 9.48683
Square Root of 1024 - √1024 = 32
Square Root of 42 - √42 = 6.48074

Square Root of 980 Solved Examples

Example 1: Solve the equation x² − 980 = 0

Solution:

x² - 980 = 0 i.e. x² = 980
x = ±√980
Since the value of the square root of 980 is 31.305,
⇒ x = +√980 or -√980 = 31.305 or -31.305.
Example 2: If the surface area of a sphere is 3920π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 3920π in²
⇒ r = ±√980 in
Since radius can't be negative,
⇒ r = √980
The square root of 980 is 31.305.
⇒ r = 31.305 in
Example 3: If the area of an equilateral triangle is 980√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 = 980√3 in²
⇒ a = ±√3920 in
Since length can't be negative,
⇒ a = √3920 = 2 √980
We know that the square root of 980 is 31.305.
⇒ a = 62.610 in

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FAQs on the Square Root of 980

What is the Value of the Square Root of 980?

The square root of 980 is 31.30495.

Why is the Square Root of 980 an Irrational Number?

Upon prime factorizing 980 i.e. 2² × 5¹ × 7², 5 is in odd power. Therefore, the square root of 980 is irrational.

What is the Square Root of 980 in Simplest Radical Form?

We need to express 980 as the product of its prime factors i.e. 980 = 2 × 2 × 5 × 7 × 7. Therefore, √980 = √2 × 2 × 5 × 7 × 7 = 14 √5. Thus, the square root of 980 in the lowest radical form is 14 √5.

What is the Square Root of -980?

The square root of -980 is an imaginary number. It can be written as √-980 = √-1 × √980 = i √980 = 31.304i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 980 is 31.305. Find the Value of the Square Root of 9.8.

Let us represent √9.8 in p/q form i.e. √(980/100) = 9.8/10 = 3.130. Hence, the value of √9.8 = 3.130

Evaluate 8 plus 6 square root 980

The given expression is 8 + 6 √980. We know that the square root of 980 is 31.305. Therefore, 8 + 6 √980 = 8 + 6 × 31.305 = 8 + 187.830 = 195.830

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