Square Root of 1215
The square root of 1215 is expressed as √1215 in the radical form and as (1215)½ or (1215)0.5 in the exponent form. The square root of 1215 rounded up to 5 decimal places is 34.85685. It is the positive solution of the equation x2 = 1215. We can express the square root of 1215 in its lowest radical form as 9 √15.
- Square Root of 1215: 34.85685011586675
- Square Root of 1215 in exponential form: (1215)½ or (1215)0.5
- Square Root of 1215 in radical form: √1215 or 9 √15
1. | What is the Square Root of 1215? |
2. | How to find the Square Root of 1215? |
3. | Is the Square Root of 1215 Irrational? |
4. | FAQs |
What is the Square Root of 1215?
The square root of 1215, (or root 1215), is the number which when multiplied by itself gives the product as 1215. Therefore, the square root of 1215 = √1215 = 9 √15 = 34.85685011586675.
☛ Check: Square Root Calculator
How to Find Square Root of 1215?
Value of √1215 by Long Division Method
Explanation:
- Forming pairs: 12 and 15
- Find a number Y (3) such that whose square is <= 12. Now divide 12 by 3 with quotient as 3.
- Bring down the next pair 15, to the right of the remainder 3. The new dividend is now 315.
- Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 4) such that 6Z × Z <= 315. After finding Z, together 6 and Z (4) form a new divisor 64 for the new dividend 315.
- Divide 315 by 64 with the quotient as 4, giving the remainder = 315 - 64 × 4 = 315 - 256 = 59.
- Now, let's find the decimal places after the quotient 34.
- Bring down 00 to the right of this remainder 59. The new dividend is now 5900.
- Add the last digit of quotient to divisor i.e. 4 + 64 = 68. To the right of 68, find a digit Z (which is 8) such that 68Z × Z <= 5900. Together they form a new divisor (688) for the new dividend (5900).
- Divide 5900 by 688 with the quotient as 8, giving the remainder = 5900 - 688 × 8 = 5900 - 5504 = 396.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1215.
Therefore, the square root of 1215 by long division method is 34.8 approximately.
Is Square Root of 1215 Irrational?
The actual value of √1215 is undetermined. The value of √1215 up to 25 decimal places is 34.85685011586675196661339. Hence, the square root of 1215 is an irrational number.
☛ Also Check:
- Square Root of 97 - √97 = 9.84886
- Square Root of 34 - √34 = 5.83095
- Square Root of 2 - √2 = 1.41421
- Square Root of 900 - √900 = 30
- Square Root of 324 - √324 = 18
- Square Root of 54 - √54 = 7.34847
- Square Root of 320 - √320 = 17.88854
Square Root of 1215 Solved Examples
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Example 1: Solve the equation x2 − 1215 = 0
Solution:
x2 - 1215 = 0 i.e. x2 = 1215
x = ±√1215
Since the value of the square root of 1215 is 34.857,
⇒ x = +√1215 or -√1215 = 34.857 or -34.857. -
Example 2: If the surface area of a sphere is 4860π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 4860π in2
⇒ r = ±√1215 in
Since radius can't be negative,
⇒ r = √1215
The square root of 1215 is 34.857.
⇒ r = 34.857 in -
Example 3: If the area of a square is 1215 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 = 1215 in2
⇒ a = ±√1215 in
Since length can't be negative,
⇒ a = √1215 = 34.857 in
FAQs on the Square Root of 1215
What is the Value of the Square Root of 1215?
The square root of 1215 is 34.85685.
Why is the Square Root of 1215 an Irrational Number?
Upon prime factorizing 1215 i.e. 35 × 51, 3 is in odd power. Therefore, the square root of 1215 is irrational.
What is the Value of 11 square root 1215?
The square root of 1215 is 34.857. Therefore, 11 √1215 = 11 × 34.857 = 383.425.
Is the number 1215 a Perfect Square?
The prime factorization of 1215 = 35 × 51. Here, the prime factor 3 is not in the pair. Therefore, 1215 is not a perfect square.
What is the Square of the Square Root of 1215?
The square of the square root of 1215 is the number 1215 itself i.e. (√1215)2 = (1215)2/2 = 1215.
What is the Square Root of 1215 in Simplest Radical Form?
We need to express 1215 as the product of its prime factors i.e. 1215 = 3 × 3 × 3 × 3 × 3 × 5. Therefore, √1215 = √3 × 3 × 3 × 3 × 3 × 5 = 9 √15. Thus, the square root of 1215 in the lowest radical form is 9 √15.
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