Square Root of 1536
The square root of 1536 is expressed as √1536 in the radical form and as (1536)½ or (1536)0.5 in the exponent form. The square root of 1536 rounded up to 6 decimal places is 39.191836. It is the positive solution of the equation x2 = 1536. We can express the square root of 1536 in its lowest radical form as 16 √6.
- Square Root of 1536: 39.191835884530846
- Square Root of 1536 in exponential form: (1536)½ or (1536)0.5
- Square Root of 1536 in radical form: √1536 or 16 √6
1. | What is the Square Root of 1536? |
2. | How to find the Square Root of 1536? |
3. | Is the Square Root of 1536 Irrational? |
4. | FAQs |
What is the Square Root of 1536?
The square root of 1536, (or root 1536), is the number which when multiplied by itself gives the product as 1536. Therefore, the square root of 1536 = √1536 = 16 √6 = 39.191835884530846.
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How to Find Square Root of 1536?
Value of √1536 by Long Division Method
Explanation:
- Forming pairs: 15 and 36
- Find a number Y (3) such that whose square is <= 15. Now divide 15 by 3 with quotient as 3.
- Bring down the next pair 36, to the right of the remainder 6. The new dividend is now 636.
- 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 9) such that 6Z × Z <= 636. After finding Z, together 6 and Z (9) form a new divisor 69 for the new dividend 636.
- Divide 636 by 69 with the quotient as 9, giving the remainder = 636 - 69 × 9 = 636 - 621 = 15.
- Now, let's find the decimal places after the quotient 39.
- Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
- Add the last digit of quotient to divisor i.e. 9 + 69 = 78. To the right of 78, find a digit Z (which is 1) such that 78Z × Z <= 1500. Together they form a new divisor (781) for the new dividend (1500).
- Divide 1500 by 781 with the quotient as 1, giving the remainder = 1500 - 781 × 1 = 1500 - 781 = 719.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1536.
Therefore, the square root of 1536 by long division method is 39.1 approx.
Is Square Root of 1536 Irrational?
The actual value of √1536 is undetermined. The value of √1536 up to 25 decimal places is 39.19183588453084957115655. Hence, the square root of 1536 is an irrational number.
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- Square Root of 361 - √361 = 19
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- Square Root of 113 - √113 = 10.63015
- Square Root of 11 - √11 = 3.31662
- Square Root of 900 - √900 = 30
- Square Root of 289 - √289 = 17
- Square Root of 45 - √45 = 6.70820
Square Root of 1536 Solved Examples
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Example 1: Solve the equation x2 − 1536 = 0
Solution:
x2 - 1536 = 0 i.e. x2 = 1536
x = ±√1536
Since the value of the square root of 1536 is 39.192,
⇒ x = +√1536 or -√1536 = 39.192 or -39.192. -
Example 2: If the surface area of a cube is 9216 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 = 9216 in2
⇒ a = ±√1536 in
Since length can't be negative,
⇒ a = √1536
We know that the square root of 1536 is 39.192.
⇒ a = 39.192 in -
Example 3: If the area of a circle is 1536π in2. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr2 = 1536π in2
⇒ r = ±√1536 in
Since radius can't be negative,
⇒ r = √1536
The square root of 1536 is 39.192.
⇒ r = 39.192 in
FAQs on the Square Root of 1536
What is the Value of the Square Root of 1536?
The square root of 1536 is 39.19183.
Why is the Square Root of 1536 an Irrational Number?
Upon prime factorizing 1536 i.e. 29 × 31, 2 is in odd power. Therefore, the square root of 1536 is irrational.
Is the number 1536 a Perfect Square?
The prime factorization of 1536 = 29 × 31. Here, the prime factor 2 is not in the pair. Therefore, 1536 is not a perfect square.
What is the Square of the Square Root of 1536?
The square of the square root of 1536 is the number 1536 itself i.e. (√1536)2 = (1536)2/2 = 1536.
What is the Square Root of -1536?
The square root of -1536 is an imaginary number. It can be written as √-1536 = √-1 × √1536 = i √1536 = 39.191i
where i = √-1 and it is called the imaginary unit.
If the Square Root of 1536 is 39.192. Find the Value of the Square Root of 15.36.
Let us represent √15.36 in p/q form i.e. √(1536/100) = 15.36/10 = 3.919. Hence, the value of √15.36 = 3.919
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