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Square Root of 476

The square root of 476 is expressed as √476 in the radical form and as (476)^½ or (476)^0.5 in the exponent form. The square root of 476 rounded up to 10 decimal places is 21.8174242293. It is the positive solution of the equation x² = 476. We can express the square root of 476 in its lowest radical form as 2 √119.

Square Root of 476: 21.817424229271428
Square Root of 476 in exponential form: (476)^½ or (476)^0.5
Square Root of 476 in radical form: √476 or 2 √119

Square Root of 476

1.	What is the Square Root of 476?
2.	How to find the Square Root of 476?
3.	Is the Square Root of 476 Irrational?
4.	FAQs

What is the Square Root of 476?

The square root of 476, (or root 476), is the number which when multiplied by itself gives the product as 476. Therefore, the square root of 476 = √476 = 2 √119 = 21.817424229271428.

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How to Find Square Root of 476?

Square Root of 476 by Long Division Method

Value of √476 by Long Division Method

Explanation:

Forming pairs: 04 and 76
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 76, to the right of the remainder 0. The new dividend is now 76.
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 <= 76. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 76.
Divide 76 by 41 with the quotient as 1, giving the remainder = 76 - 41 × 1 = 76 - 41 = 35.
Now, let's find the decimal places after the quotient 21.
Bring down 00 to the right of this remainder 35. The new dividend is now 3500.
Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 8) such that 42Z × Z <= 3500. Together they form a new divisor (428) for the new dividend (3500).
Divide 3500 by 428 with the quotient as 8, giving the remainder = 3500 - 428 × 8 = 3500 - 3424 = 76.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 476.

Therefore, the square root of 476 by long division method is 21.8 approximately.

Is Square Root of 476 Irrational?

The actual value of √476 is undetermined. The value of √476 up to 25 decimal places is 21.81742422927142882300431. Hence, the square root of 476 is an irrational number.

☛ Also Check:

Square Root of 225 - √225 = 15
Square Root of 44 - √44 = 6.63325
Square Root of 68 - √68 = 8.24621
Square Root of 1024 - √1024 = 32
Square Root of 21 - √21 = 4.58258
Square Root of 92 - √92 = 9.59166
Square Root of 240 - √240 = 15.49193

Square Root of 476 Solved Examples

Example 1: Solve the equation x² − 476 = 0

Solution:

x² - 476 = 0 i.e. x² = 476
x = ±√476
Since the value of the square root of 476 is 21.817,
⇒ x = +√476 or -√476 = 21.817 or -21.817.
Example 2: If the surface area of a cube is 2856 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 = 2856 in²
⇒ a = ±√476 in
Since length can't be negative,
⇒ a = √476
We know that the square root of 476 is 21.817.
⇒ a = 21.817 in
Example 3: If the area of a square is 476 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 = 476 in²
⇒ a = ±√476 in
Since length can't be negative,
⇒ a = √476 = 21.817 in

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FAQs on the Square Root of 476

What is the Value of the Square Root of 476?

The square root of 476 is 21.81742.

Why is the Square Root of 476 an Irrational Number?

Upon prime factorizing 476 i.e. 2² × 7¹ × 17¹, 7 is in odd power. Therefore, the square root of 476 is irrational.

If the Square Root of 476 is 21.817. Find the Value of the Square Root of 4.76.

Let us represent √4.76 in p/q form i.e. √(476/100) = 4.76/10 = 2.182. Hence, the value of √4.76 = 2.182

Is the number 476 a Perfect Square?

The prime factorization of 476 = 2² × 7¹ × 17¹. Here, the prime factor 7 is not in the pair. Therefore, 476 is not a perfect square.

Evaluate 5 plus 6 square root 476

The given expression is 5 + 6 √476. We know that the square root of 476 is 21.817. Therefore, 5 + 6 √476 = 5 + 6 × 21.817 = 5 + 130.905 = 135.905

What is the Square Root of 476 in Simplest Radical Form?

We need to express 476 as the product of its prime factors i.e. 476 = 2 × 2 × 7 × 17. Therefore, √476 = √2 × 2 × 7 × 17 = 2 √119. Thus, the square root of 476 in the lowest radical form is 2 √119.

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