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Square Root of 480

The square root of 480 is expressed as √480 in the radical form and as (480)^½ or (480)^0.5 in the exponent form. The square root of 480 rounded up to 6 decimal places is 21.908902. It is the positive solution of the equation x² = 480. We can express the square root of 480 in its lowest radical form as 4 √30.

Square Root of 480: 21.908902300206645
Square Root of 480 in exponential form: (480)^½ or (480)^0.5
Square Root of 480 in radical form: √480 or 4 √30

Square Root of 480

1.	What is the Square Root of 480?
2.	How to find the Square Root of 480?
3.	Is the Square Root of 480 Irrational?
4.	FAQs

What is the Square Root of 480?

The square root of 480, (or root 480), is the number which when multiplied by itself gives the product as 480. Therefore, the square root of 480 = √480 = 4 √30 = 21.908902300206645.

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How to Find Square Root of 480?

Square Root of 480 by Long Division Method

Value of √480 by Long Division Method

Explanation:

Forming pairs: 04 and 80
Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
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 (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 1) such that 4Z × Z <= 80. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 80.
Divide 80 by 41 with the quotient as 1, giving the remainder = 80 - 41 × 1 = 80 - 41 = 39.
Now, let's find the decimal places after the quotient 21.
Bring down 00 to the right of this remainder 39. The new dividend is now 3900.
Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 9) such that 42Z × Z <= 3900. Together they form a new divisor (429) for the new dividend (3900).
Divide 3900 by 429 with the quotient as 9, giving the remainder = 3900 - 429 × 9 = 3900 - 3861 = 39.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 480.

Therefore, the square root of 480 by long division method is 21.9 approximately.

Is Square Root of 480 Irrational?

The actual value of √480 is undetermined. The value of √480 up to 25 decimal places is 21.90890230020664453827879. Hence, the square root of 480 is an irrational number.

☛ Also Check:

Square Root of 49 - √49 = 7
Square Root of 14 - √14 = 3.74166
Square Root of 1000 - √1000 = 31.62278
Square Root of 44 - √44 = 6.63325
Square Root of 48 - √48 = 6.92820
Square Root of 92 - √92 = 9.59166
Square Root of 8 - √8 = 2.82843

Square Root of 480 Solved Examples

Example 1: Solve the equation x² − 480 = 0

Solution:

x² - 480 = 0 i.e. x² = 480
x = ±√480
Since the value of the square root of 480 is 21.909,
⇒ x = +√480 or -√480 = 21.909 or -21.909.
Example 2: If the area of a square is 480 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 = 480 in²
⇒ a = ±√480 in
Since length can't be negative,
⇒ a = √480 = 21.909 in
Example 3: If the surface area of a cube is 2880 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 = 2880 in²
⇒ a = ±√480 in
Since length can't be negative,
⇒ a = √480
We know that the square root of 480 is 21.909.
⇒ a = 21.909 in

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FAQs on the Square Root of 480

What is the Value of the Square Root of 480?

The square root of 480 is 21.9089.

Why is the Square Root of 480 an Irrational Number?

Upon prime factorizing 480 i.e. 2⁵ × 3¹ × 5¹, 2 is in odd power. Therefore, the square root of 480 is irrational.

Evaluate 3 plus 15 square root 480

The given expression is 3 + 15 √480. We know that the square root of 480 is 21.909. Therefore, 3 + 15 √480 = 3 + 15 × 21.909 = 3 + 328.634 = 331.634

If the Square Root of 480 is 21.909. Find the Value of the Square Root of 4.8.

Let us represent √4.8 in p/q form i.e. √(480/100) = 4.8/10 = 2.191. Hence, the value of √4.8 = 2.191

What is the Square of the Square Root of 480?

The square of the square root of 480 is the number 480 itself i.e. (√480)² = (480)^2/2 = 480.

Is the number 480 a Perfect Square?

The prime factorization of 480 = 2⁵ × 3¹ × 5¹. Here, the prime factor 2 is not in the pair. Therefore, 480 is not a perfect square.

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