Square Root of 496
The square root of 496 is expressed as √496 in the radical form and as (496)^{½} or (496)^{0.5} in the exponent form. The square root of 496 rounded up to 5 decimal places is 22.27106. It is the positive solution of the equation x^{2} = 496. We can express the square root of 496 in its lowest radical form as 4 √31.
 Square Root of 496: 22.271057451320086
 Square Root of 496 in exponential form: (496)^{½} or (496)^{0.5}
 Square Root of 496 in radical form: √496 or 4 √31
1.  What is the Square Root of 496? 
2.  How to find the Square Root of 496? 
3.  Is the Square Root of 496 Irrational? 
4.  FAQs 
What is the Square Root of 496?
The square root of 496, (or root 496), is the number which when multiplied by itself gives the product as 496. Therefore, the square root of 496 = √496 = 4 √31 = 22.271057451320086.
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How to Find Square Root of 496?
Value of √496 by Long Division Method
Explanation:
 Forming pairs: 04 and 96
 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 96, to the right of the remainder 0. The new dividend is now 96.
 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 2) such that 4Z × Z <= 96. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 96.
 Divide 96 by 42 with the quotient as 2, giving the remainder = 96  42 × 2 = 96  84 = 12.
 Now, let's find the decimal places after the quotient 22.
 Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
 Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 2) such that 44Z × Z <= 1200. Together they form a new divisor (442) for the new dividend (1200).
 Divide 1200 by 442 with the quotient as 2, giving the remainder = 1200  442 × 2 = 1200  884 = 316.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 496.
Therefore, the square root of 496 by long division method is 22.2 approx.
Is Square Root of 496 Irrational?
The actual value of √496 is undetermined. The value of √496 up to 25 decimal places is 22.27105745132008768847789. Hence, the square root of 496 is an irrational number.
☛ Also Check:
 Square Root of 676  √676 = 26
 Square Root of 12  √12 = 3.46410
 Square Root of 96  √96 = 9.79796
 Square Root of 26  √26 = 5.09902
 Square Root of 22  √22 = 4.69042
 Square Root of 196  √196 = 14
 Square Root of 16  √16 = 4
Square Root of 496 Solved Examples

Example 1: Solve the equation x^{2} − 496 = 0
Solution:
x^{2}  496 = 0 i.e. x^{2} = 496
x = ±√496
Since the value of the square root of 496 is 22.271,
⇒ x = +√496 or √496 = 22.271 or 22.271. 
Example 2: If the area of a square is 496 in^{2}. 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 = a^{2} = 496 in^{2}
⇒ a = ±√496 in
Since length can't be negative,
⇒ a = √496 = 22.271 in 
Example 3: If the area of an equilateral triangle is 496√3 in^{2}. 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)a^{2} = 496√3 in^{2}
⇒ a = ±√1984 in
Since length can't be negative,
⇒ a = √1984 = 2 √496
We know that the square root of 496 is 22.271.
⇒ a = 44.542 in
FAQs on the Square Root of 496
What is the Value of the Square Root of 496?
The square root of 496 is 22.27105.
Why is the Square Root of 496 an Irrational Number?
Upon prime factorizing 496 i.e. 2^{4} × 31^{1}, 31 is in odd power. Therefore, the square root of 496 is irrational.
What is the Square of the Square Root of 496?
The square of the square root of 496 is the number 496 itself i.e. (√496)^{2} = (496)^{2/2} = 496.
What is the Value of 16 square root 496?
The square root of 496 is 22.271. Therefore, 16 √496 = 16 × 22.271 = 356.337.
What is the Square Root of 496 in Simplest Radical Form?
We need to express 496 as the product of its prime factors i.e. 496 = 2 × 2 × 2 × 2 × 31. Therefore, √496 = √2 × 2 × 2 × 2 × 31 = 4 √31. Thus, the square root of 496 in the lowest radical form is 4 √31.
If the Square Root of 496 is 22.271. Find the Value of the Square Root of 4.96.
Let us represent √4.96 in p/q form i.e. √(496/100) = 4.96/10 = 2.227. Hence, the value of √4.96 = 2.227
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