Square Root of 425
The square root of 425 is expressed as √425 in the radical form and as (425)½ or (425)0.5 in the exponent form. The square root of 425 rounded up to 8 decimal places is 20.61552813. It is the positive solution of the equation x2 = 425. We can express the square root of 425 in its lowest radical form as 5 √17.
- Square Root of 425: 20.615528128088304
- Square Root of 425 in exponential form: (425)½ or (425)0.5
- Square Root of 425 in radical form: √425 or 5 √17
1. | What is the Square Root of 425? |
2. | How to find the Square Root of 425? |
3. | Is the Square Root of 425 Irrational? |
4. | FAQs |
What is the Square Root of 425?
The square root of 425, (or root 425), is the number which when multiplied by itself gives the product as 425. Therefore, the square root of 425 = √425 = 5 √17 = 20.615528128088304.
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How to Find Square Root of 425?
Value of √425 by Long Division Method
Explanation:
- Forming pairs: 04 and 25
- 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 25, to the right of the remainder 0. The new dividend is now 25.
- 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 0) such that 4Z × Z <= 25. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 25.
- Divide 25 by 40 with the quotient as 0, giving the remainder = 25 - 40 × 0 = 25 - 0 = 25.
- Now, let's find the decimal places after the quotient 20.
- Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
- Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 6) such that 40Z × Z <= 2500. Together they form a new divisor (406) for the new dividend (2500).
- Divide 2500 by 406 with the quotient as 6, giving the remainder = 2500 - 406 × 6 = 2500 - 2436 = 64.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 425.
Therefore, the square root of 425 by long division method is 20.6 approx.
Is Square Root of 425 Irrational?
The actual value of √425 is undetermined. The value of √425 up to 25 decimal places is 20.61552812808830274910705. Hence, the square root of 425 is an irrational number.
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- Square Root of 11 - √11 = 3.31662
- Square Root of 1681 - √1681 = 41
- Square Root of 45 - √45 = 6.70820
- Square Root of 14 - √14 = 3.74166
Square Root of 425 Solved Examples
-
Example 1: Solve the equation x2 − 425 = 0
Solution:
x2 - 425 = 0 i.e. x2 = 425
x = ±√425
Since the value of the square root of 425 is 20.616,
⇒ x = +√425 or -√425 = 20.616 or -20.616. -
Example 2: If the area of a square is 425 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 = 425 in2
⇒ a = ±√425 in
Since length can't be negative,
⇒ a = √425 = 20.616 in -
Example 3: If the surface area of a sphere is 1700π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 1700π in2
⇒ r = ±√425 in
Since radius can't be negative,
⇒ r = √425
The square root of 425 is 20.616.
⇒ r = 20.616 in
FAQs on the Square Root of 425
What is the Value of the Square Root of 425?
The square root of 425 is 20.61552.
Why is the Square Root of 425 an Irrational Number?
Upon prime factorizing 425 i.e. 52 × 171, 17 is in odd power. Therefore, the square root of 425 is irrational.
What is the Square of the Square Root of 425?
The square of the square root of 425 is the number 425 itself i.e. (√425)2 = (425)2/2 = 425.
What is the Square Root of -425?
The square root of -425 is an imaginary number. It can be written as √-425 = √-1 × √425 = i √425 = 20.615i
where i = √-1 and it is called the imaginary unit.
If the Square Root of 425 is 20.616. Find the Value of the Square Root of 4.25.
Let us represent √4.25 in p/q form i.e. √(425/100) = 4.25/10 = 2.062. Hence, the value of √4.25 = 2.062
What is the Square Root of 425 in Simplest Radical Form?
We need to express 425 as the product of its prime factors i.e. 425 = 5 × 5 × 17. Therefore, √425 = √5 × 5 × 17 = 5 √17. Thus, the square root of 425 in the lowest radical form is 5 √17.
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