Square Root of 629
The square root of 629 is expressed as √629 in the radical form and as (629)½ or (629)0.5 in the exponent form. The square root of 629 rounded up to 7 decimal places is 25.0798724. It is the positive solution of the equation x2 = 629.
- Square Root of 629: 25.079872407968907
- Square Root of 629 in exponential form: (629)½ or (629)0.5
- Square Root of 629 in radical form: √629
1. | What is the Square Root of 629? |
2. | How to find the Square Root of 629? |
3. | Is the Square Root of 629 Irrational? |
4. | FAQs |
What is the Square Root of 629?
The square root of 629, (or root 629), is the number which when multiplied by itself gives the product as 629. Therefore, the square root of 629 = √629 = 25.079872407968907.
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How to Find Square Root of 629?
Value of √629 by Long Division Method
Explanation:
- Forming pairs: 06 and 29
- 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 29, to the right of the remainder 2. The new dividend is now 229.
- 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 5) such that 4Z × Z <= 229. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 229.
- Divide 229 by 45 with the quotient as 5, giving the remainder = 229 - 45 × 5 = 229 - 225 = 4.
- Now, let's find the decimal places after the quotient 25.
- Bring down 00 to the right of this remainder 4. The new dividend is now 400.
- Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 0) such that 50Z × Z <= 400. Together they form a new divisor (500) for the new dividend (400).
- Divide 400 by 500 with the quotient as 0, giving the remainder = 400 - 500 × 0 = 400 - 0 = 400.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 629.
Therefore, the square root of 629 by long division method is 25.0 approximately.
Is Square Root of 629 Irrational?
The actual value of √629 is undetermined. The value of √629 up to 25 decimal places is 25.07987240796890497609742. Hence, the square root of 629 is an irrational number.
☛ Also Check:
- Square Root of 98 - √98 = 9.89949
- Square Root of 60 - √60 = 7.74597
- Square Root of 12 - √12 = 3.46410
- Square Root of 22 - √22 = 4.69042
- Square Root of 100 - √100 = 10
- Square Root of 1681 - √1681 = 41
- Square Root of 400 - √400 = 20
Square Root of 629 Solved Examples
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Example 1: Solve the equation x2 − 629 = 0
Solution:
x2 - 629 = 0 i.e. x2 = 629
x = ±√629
Since the value of the square root of 629 is 25.080,
⇒ x = +√629 or -√629 = 25.080 or -25.080. -
Example 2: If the area of a circle is 629π in2. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr2 = 629π in2
⇒ r = ±√629 in
Since radius can't be negative,
⇒ r = √629
The square root of 629 is 25.080.
⇒ r = 25.080 in -
Example 3: If the surface area of a sphere is 2516π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 2516π in2
⇒ r = ±√629 in
Since radius can't be negative,
⇒ r = √629
The square root of 629 is 25.080.
⇒ r = 25.080 in
FAQs on the Square Root of 629
What is the Value of the Square Root of 629?
The square root of 629 is 25.07987.
Why is the Square Root of 629 an Irrational Number?
Upon prime factorizing 629 i.e. 171 × 371, 17 is in odd power. Therefore, the square root of 629 is irrational.
If the Square Root of 629 is 25.080. Find the Value of the Square Root of 6.29.
Let us represent √6.29 in p/q form i.e. √(629/100) = 6.29/10 = 2.508. Hence, the value of √6.29 = 2.508
What is the Value of 16 square root 629?
The square root of 629 is 25.080. Therefore, 16 √629 = 16 × 25.080 = 401.278.
Evaluate 7 plus 19 square root 629
The given expression is 7 + 19 √629. We know that the square root of 629 is 25.080. Therefore, 7 + 19 √629 = 7 + 19 × 25.080 = 7 + 476.518 = 483.518
What is the Square of the Square Root of 629?
The square of the square root of 629 is the number 629 itself i.e. (√629)2 = (629)2/2 = 629.
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