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What is square root of 704 over 11

User Baa
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1 Answer

2 votes

Answer:


\huge\boxed{8}

Explanation:

We can simplify the radical over the fraction:


\sqrt{(704)/(11)}

by expanding the numerator.

We know that the prime factorization (the simplest representation of a number as a product of prime numbers) of 704 is:


\begin{aligned}704 &= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 11\\ &= 2^6 \cdot 11\end{aligned}

Therefore, we can replace 704 with its prime factorization in the radical:


\sqrt{(2^6\cdot 11)/(11)}

Now, we can see that the 11's cancel in the numerator and denominator:


\sqrt{(2^6\cdot \!\\ot\!\!11)/(\\ot\!\!11)}


√(2^6)

Finally, we can evaluate the square root.


√(2^6) = 2^3 =\huge\boxed{8}

User Fzgregor
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