Calculating the Square Root of 576
The question asks for the value that, when multiplied by itself, equals 576. This is known as finding the square root of 576, denoted mathematically as $\sqrt{576}$.
Method: Prime Factorization
We can find the square root by breaking down 576 into its prime factors:
- Start dividing 576 by the smallest prime number, 2:
- $576 \div 2 = 288$
- $288 \div 2 = 144$
- $144 \div 2 = 72$
- $72 \div 2 = 36$
- $36 \div 2 = 18$
- $18 \div 2 = 9$
- Now, divide by the next prime number, 3:
- $9 \div 3 = 3$
- $3 \div 3 = 1$
The prime factorization of 576 is $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$, or $2^6 \times 3^2$.
Finding the Square Root Value
To find the square root, we take half of the exponent for each prime factor:
- $\sqrt{576} = \sqrt{2^6 \times 3^2}$
- $= 2^{6/2} \times 3^{2/2}$
- $= 2^3 \times 3^1$
- $= (2 \times 2 \times 2) \times 3$
- $= 8 \times 3$
- $= 24$
Therefore, the square root of 576 is 24.
Final Answer: The final answer is 24
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Important Questions from Square and Square Root
The addition of the squares of two numbers in squares is 221. What are those numbers?
Find the value of \(\sqrt{9604} \).
If (584)2 = 341056, then the value of square root of 34.1056 is:
Which one of the following numbers is not a square of any natural number?
The value of \(\sqrt{72+\sqrt{72 +\sqrt{72+.....\infty}}}\) is :
