In Mathematics, the square root of 216 is a number, which when multiplied by itself results in the original number 216. The value of the square root of 216 is not a rational number as it cannot be expressed in the form of p/q. The square root of 216 can be found using two different methods, such as long division and prime factorization methods. In this article, we are going to learn the square root of 216 in decimal form, radical form and the procedure to find the value of square root 216 using the two different methods in detail.
What is the Value of Square Root of 216?
If a number is multiplied by itself and gives the result as 216, then the number is the square root 216. The square root of 216 is symbolically expressed as √216.
Hence, √216 = √(Value × Value)
Thus, if we multiply the number 14.697 two times, we get the original value 216.
(i.e) √216 = √(14.697×14.697)
√216 = √(14.697)2
Now, remove square and square root, we get
√216 = ± 14.6969 (or)
√216 = ± 14.697 (Rounded to three decimal places)
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Square Root of 216 in Decimal Form: 14.697. |
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Square Root of 216 in Radical Form
The square root of 216 can be expressed in the radical form. The radical form of the value of the square root can be written if we know the prime factorisation of 216. We know that the prime factorisation of 216 is 23 × 33. Therefore, the simplest radical form of value of the square root of 216 is √(23 × 33), which is equal to 6√6.
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Square Root of 216 in Radical Form: 6√6. |
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Square Root of 216 by Prime Factorization Method
To find the square root of 216 using the prime factorization method, we need to know the prime factorisation of 216. The prime factorisation of 216 is 2 × 2 × 2 × 3 × 3 × 3.
Thus, √216 = √(2 × 2 × 2 × 3 × 3 × 3)
√216 = √[(2 × 2) × (2 × 3) × (3 × 3)]
√216 = √(2)2.√6. √(3)2
On cancelling square and square root, we get
√216 = (2×3).√6 = 6√6
We know that,
√6 = 2.44948
Now, substitute the values of √6 in the above equation, we get
√216 = 6 × 2.44948
√216 = 14.6969 (approximately)
Hence, the square root of 216 in decimal form is 14.697(rounded to three decimal places)
Square Root of 216 by Long Division Method
The procedure to find the square root of 216 using the long division method is given as follows:
Step 1: Write the number 216 in decimal form. To find the exact value of the square root of 216, add 4 zeros after the decimal point. Hence, 216 in decimal form is 216.0000. Now, pair the number 216 from right to left by putting the bar on the top of the number.
Step 2: Now, divide the number 2 by a number, such that the product of the same number should be less than or equal to 2. Thus, 1×1 = 1, which is less than 2. Thus, we obtained the quotient = 1 and remainder = 1.
Step 3: Double the quotient value, so we get 2, and assume that 20 is the new divisor. Now, bring down the value 16 for division operation. So, the new dividend obtained is 116. Now, find the number, such that (20 + new number) × new number should give the product value, that should be less than or equal to 116. Hence, (20+4) × 4 = 96, which is less than 116.
Step 4: Now subtract 96 from 116, and we get 20 as the new remainder and 14 as a quotient.
Step 5: The new quotient obtained is 14, and double that. Hence, we get 28 and assume that 280 is our new divisor. Now, bring down the two zeros and, we have 2000 as the new dividend.
Step 6: Find the number, such that (280 + new number) × new number should give the product value, that should be less than or equal to 2000. Thus, (280+6)× 6 =1716, which is less than 2000.
Step 7: Subtract 1716 from 2000, and we get 284 as the new reminder.
Step 8: Continue this process until we get the approximate value of the square root of 216 up to three decimal places. (Note: keep the decimal point in the quotient value after bringing down all the values in the dividend).
Step 9: Thus, the approximate value of the square root of 216, √216 is 14.697 (rounded to 3 decimal places).
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Visualising square roots
Finding Square roots
Examples
Example 1:
Simplify √6.√216.
Solution:
Given: √6 .√216.
We know that the square root of 216 in radical form is 6√6.
Now, substitute the value in the expression, we get:
√6 .√216 = √6(6√6)
√6. √216 = 6(6) = 36
Therefore, √6. √216 is 36.
Example 2:
Find the value of x, if 5x + √216 = 90
Solution:
Given equation: 5x + √216 = 90…(1)
We know that √216 is approximately equal to 14.697.
Now, substitute the value in equation (1),
5x + 14.697 = 90
5x = 90-14.697
5x = 75.303
x = 75.303/5
x = 15.0606
Therefore, the value of x is 15.0606.
Frequently Asked Questions on Square Root of 216
What is the value of the square root of 216?
The value of the square root of 216 is approximately equal to 14.697, which is rounded to three decimal places.
What is the square root of 216 in radical form?
The square root of 216 in radical form is 6√6.
Is the square root of 216 a rational number?
No, the square root of 216 is not a rational number as it cannot be expressed in the form of p/q.
Is 216 a perfect square?
No, 216 is not a perfect cube, as it cannot be expressed as the product of two equal integers.
What is the value of the square of square root of 216?
The value of the square of square root of 216 is 216.
Square of the square root of 216 means (√216)2. On cancelling square and square root, we get,
(√216)2 = 216.
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