Square Root of 616
The square root of 616 is expressed as √616 in the radical form and as (616)½ or (616)0.5 in the exponent form. The square root of 616 rounded up to 9 decimal places is 24.819347292. It is the positive solution of the equation x2 = 616. We can express the square root of 616 in its lowest radical form as 2 √154.
- Square Root of 616: 24.819347291981714
- Square Root of 616 in exponential form: (616)½ or (616)0.5
- Square Root of 616 in radical form: √616 or 2 √154
1. | What is the Square Root of 616? |
2. | How to find the Square Root of 616? |
3. | Is the Square Root of 616 Irrational? |
4. | FAQs |
What is the Square Root of 616?
The square root of 616, (or root 616), is the number which when multiplied by itself gives the product as 616. Therefore, the square root of 616 = √616 = 2 √154 = 24.819347291981714.
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How to Find Square Root of 616?
Value of √616 by Long Division Method
Explanation:
- Forming pairs: 06 and 16
- Find a number Y (2) such that whose square is <= 6. Now divide 06 by 2 with quotient as 2.
- Bring down the next pair 16, to the right of the remainder 2. The new dividend is now 216.
- 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 4) such that 4Z × Z <= 216. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 216.
- Divide 216 by 44 with the quotient as 4, giving the remainder = 216 - 44 × 4 = 216 - 176 = 40.
- Now, let's find the decimal places after the quotient 24.
- Bring down 00 to the right of this remainder 40. The new dividend is now 4000.
- Add the last digit of quotient to divisor i.e. 4 + 44 = 48. To the right of 48, find a digit Z (which is 8) such that 48Z × Z <= 4000. Together they form a new divisor (488) for the new dividend (4000).
- Divide 4000 by 488 with the quotient as 8, giving the remainder = 4000 - 488 × 8 = 4000 - 3904 = 96.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 616.
Therefore, the square root of 616 by long division method is 24.8 approx.
Is Square Root of 616 Irrational?
The actual value of √616 is undetermined. The value of √616 up to 25 decimal places is 24.81934729198171319226648. Hence, the square root of 616 is an irrational number.
☛ Also Check:
- Square Root of 240 - √240 = 15.49193
- Square Root of 28 - √28 = 5.29150
- Square Root of 33 - √33 = 5.74456
- Square Root of 50 - √50 = 7.07107
- Square Root of 11 - √11 = 3.31662
- Square Root of 42 - √42 = 6.48074
- Square Root of 51 - √51 = 7.14143
Square Root of 616 Solved Examples
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Example 1: Solve the equation x2 − 616 = 0
Solution:
x2 - 616 = 0 i.e. x2 = 616
x = ±√616
Since the value of the square root of 616 is 24.819,
⇒ x = +√616 or -√616 = 24.819 or -24.819. -
Example 2: If the area of an equilateral triangle is 616√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 = 616√3 in2
⇒ a = ±√2464 in
Since length can't be negative,
⇒ a = √2464 = 2 √616
We know that the square root of 616 is 24.819.
⇒ a = 49.639 in -
Example 3: If the surface area of a sphere is 2464π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 2464π in2
⇒ r = ±√616 in
Since radius can't be negative,
⇒ r = √616
The square root of 616 is 24.819.
⇒ r = 24.819 in
FAQs on the Square Root of 616
What is the Value of the Square Root of 616?
The square root of 616 is 24.81934.
Why is the Square Root of 616 an Irrational Number?
Upon prime factorizing 616 i.e. 23 × 71 × 111, 2 is in odd power. Therefore, the square root of 616 is irrational.
Is the number 616 a Perfect Square?
The prime factorization of 616 = 23 × 71 × 111. Here, the prime factor 2 is not in the pair. Therefore, 616 is not a perfect square.
If the Square Root of 616 is 24.819. Find the Value of the Square Root of 6.16.
Let us represent √6.16 in p/q form i.e. √(616/100) = 6.16/10 = 2.482. Hence, the value of √6.16 = 2.482
What is the Square Root of 616 in Simplest Radical Form?
We need to express 616 as the product of its prime factors i.e. 616 = 2 × 2 × 2 × 7 × 11. Therefore, √616 = √2 × 2 × 2 × 7 × 11 = 2 √154. Thus, the square root of 616 in the lowest radical form is 2 √154.
What is the Square Root of -616?
The square root of -616 is an imaginary number. It can be written as √-616 = √-1 × √616 = i √616 = 24.819i
where i = √-1 and it is called the imaginary unit.
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