Square Root of 9000
The square root of 9000 is expressed as √9000 in the radical form and as (9000)½ or (9000)0.5 in the exponent form. The square root of 9000 rounded up to 5 decimal places is 94.86833. It is the positive solution of the equation x2 = 9000. We can express the square root of 9000 in its lowest radical form as 30 √10.
- Square Root of 9000: 94.86832980505137
- Square Root of 9000 in exponential form: (9000)½ or (9000)0.5
- Square Root of 9000 in radical form: √9000 or 30 √10
1. | What is the Square Root of 9000? |
2. | How to find the Square Root of 9000? |
3. | Is the Square Root of 9000 Irrational? |
4. | FAQs |
What is the Square Root of 9000?
The square root of 9000, (or root 9000), is the number which when multiplied by itself gives the product as 9000. Therefore, the square root of 9000 = √9000 = 30 √10 = 94.86832980505137.
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How to Find Square Root of 9000?
Value of √9000 by Long Division Method
Explanation:
- Forming pairs: 90 and 00
- Find a number Y (9) such that whose square is <= 90. Now divide 90 by 9 with quotient as 9.
- Bring down the next pair 00, to the right of the remainder 9. The new dividend is now 900.
- Add the last digit of the quotient (9) to the divisor (9) i.e. 9 + 9 = 18. To the right of 18, find a digit Z (which is 4) such that 18Z × Z <= 900. After finding Z, together 18 and Z (4) form a new divisor 184 for the new dividend 900.
- Divide 900 by 184 with the quotient as 4, giving the remainder = 900 - 184 × 4 = 900 - 736 = 164.
- Now, let's find the decimal places after the quotient 94.
- Bring down 00 to the right of this remainder 164. The new dividend is now 16400.
- Add the last digit of quotient to divisor i.e. 4 + 184 = 188. To the right of 188, find a digit Z (which is 8) such that 188Z × Z <= 16400. Together they form a new divisor (1888) for the new dividend (16400).
- Divide 16400 by 1888 with the quotient as 8, giving the remainder = 16400 - 1888 × 8 = 16400 - 15104 = 1296.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 9000.
Therefore, the square root of 9000 by long division method is 94.8 approx.
Is Square Root of 9000 Irrational?
The actual value of √9000 is undetermined. The value of √9000 up to 25 decimal places is 94.86832980505137995996681. Hence, the square root of 9000 is an irrational number.
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- Square Root of 361 - √361 = 19
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- Square Root of 29 - √29 = 5.38516
- Square Root of 240 - √240 = 15.49193
- Square Root of 52 - √52 = 7.21110
- Square Root of 41 - √41 = 6.40312
Square Root of 9000 Solved Examples
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Example 1: Solve the equation x2 − 9000 = 0
Solution:
x2 - 9000 = 0 i.e. x2 = 9000
x = ±√9000
Since the value of the square root of 9000 is 94.868,
⇒ x = +√9000 or -√9000 = 94.868 or -94.868. -
Example 2: If the surface area of a sphere is 36000π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 36000π in2
⇒ r = ±√9000 in
Since radius can't be negative,
⇒ r = √9000
The square root of 9000 is 94.868.
⇒ r = 94.868 in -
Example 3: If the surface area of a cube is 54000 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 = 54000 in2
⇒ a = ±√9000 in
Since length can't be negative,
⇒ a = √9000
We know that the square root of 9000 is 94.868.
⇒ a = 94.868 in
FAQs on the Square Root of 9000
What is the Value of the Square Root of 9000?
The square root of 9000 is 94.86832.
Why is the Square Root of 9000 an Irrational Number?
Upon prime factorizing 9000 i.e. 23 × 32 × 53, 2 is in odd power. Therefore, the square root of 9000 is irrational.
What is the Square of the Square Root of 9000?
The square of the square root of 9000 is the number 9000 itself i.e. (√9000)2 = (9000)2/2 = 9000.
If the Square Root of 9000 is 94.868. Find the Value of the Square Root of 90.
Let us represent √90 in p/q form i.e. √(9000/100) = 90/10 = 9.487. Hence, the value of √90.0 = 9.487
What is the Square Root of 9000 in Simplest Radical Form?
We need to express 9000 as the product of its prime factors i.e. 9000 = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5. Therefore, √9000 = √2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 = 30 √10. Thus, the square root of 9000 in the lowest radical form is 30 √10.
Is the number 9000 a Perfect Square?
The prime factorization of 9000 = 23 × 32 × 53. Here, the prime factor 2 is not in the pair. Therefore, 9000 is not a perfect square.
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