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Square Root of 456

The square root of 456 is expressed as √456 in the radical form and as (456)^½ or (456)^0.5 in the exponent form. The square root of 456 rounded up to 7 decimal places is 21.3541565. It is the positive solution of the equation x² = 456. We can express the square root of 456 in its lowest radical form as 2 √114.

Square Root of 456: 21.354156504062622
Square Root of 456 in exponential form: (456)^½ or (456)^0.5
Square Root of 456 in radical form: √456 or 2 √114

Square Root of 456

1.	What is the Square Root of 456?
2.	How to find the Square Root of 456?
3.	Is the Square Root of 456 Irrational?
4.	FAQs

What is the Square Root of 456?

The square root of 456, (or root 456), is the number which when multiplied by itself gives the product as 456. Therefore, the square root of 456 = √456 = 2 √114 = 21.354156504062622.

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How to Find Square Root of 456?

Square Root of 456 by Long Division Method

Value of √456 by Long Division Method

Explanation:

Forming pairs: 04 and 56
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 56, to the right of the remainder 0. The new dividend is now 56.
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 <= 56. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 56.
Divide 56 by 41 with the quotient as 1, giving the remainder = 56 - 41 × 1 = 56 - 41 = 15.
Now, let's find the decimal places after the quotient 21.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 3) such that 42Z × Z <= 1500. Together they form a new divisor (423) for the new dividend (1500).
Divide 1500 by 423 with the quotient as 3, giving the remainder = 1500 - 423 × 3 = 1500 - 1269 = 231.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 456.

Therefore, the square root of 456 by long division method is 21.3 approx.

Is Square Root of 456 Irrational?

The actual value of √456 is undetermined. The value of √456 up to 25 decimal places is 21.35415650406262242162305. Hence, the square root of 456 is an irrational number.

☛ Also Check:

Square Root of 200 - √200 = 14.14214
Square Root of 37 - √37 = 6.08276
Square Root of 89 - √89 = 9.43398
Square Root of 106 - √106 = 10.29563
Square Root of 900 - √900 = 30
Square Root of 1521 - √1521 = 39
Square Root of 16 - √16 = 4

Square Root of 456 Solved Examples

Example 1: Solve the equation x² − 456 = 0

Solution:

x² - 456 = 0 i.e. x² = 456
x = ±√456
Since the value of the square root of 456 is 21.354,
⇒ x = +√456 or -√456 = 21.354 or -21.354.
Example 2: If the area of a circle is 456π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 456π in²
⇒ r = ±√456 in
Since radius can't be negative,
⇒ r = √456
The square root of 456 is 21.354.
⇒ r = 21.354 in
Example 3: If the surface area of a cube is 2736 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 = 2736 in²
⇒ a = ±√456 in
Since length can't be negative,
⇒ a = √456
We know that the square root of 456 is 21.354.
⇒ a = 21.354 in

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FAQs on the Square Root of 456

What is the Value of the Square Root of 456?

The square root of 456 is 21.35415.

Why is the Square Root of 456 an Irrational Number?

Upon prime factorizing 456 i.e. 2³ × 3¹ × 19¹, 2 is in odd power. Therefore, the square root of 456 is irrational.

What is the Value of 10 square root 456?

The square root of 456 is 21.354. Therefore, 10 √456 = 10 × 21.354 = 213.542.

Is the number 456 a Perfect Square?

The prime factorization of 456 = 2³ × 3¹ × 19¹. Here, the prime factor 2 is not in the pair. Therefore, 456 is not a perfect square.

What is the Square Root of 456 in Simplest Radical Form?

We need to express 456 as the product of its prime factors i.e. 456 = 2 × 2 × 2 × 3 × 19. Therefore, √456 = √2 × 2 × 2 × 3 × 19 = 2 √114. Thus, the square root of 456 in the lowest radical form is 2 √114.

If the Square Root of 456 is 21.354. Find the Value of the Square Root of 4.56.

Let us represent √4.56 in p/q form i.e. √(456/100) = 4.56/10 = 2.135. Hence, the value of √4.56 = 2.135

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