What is square root of 704 over 11

Question

asked Jul 25, 2024 6.6k views

1 Answer

Fzgregor · Answer 1 · 2024-07-31T20:24:08+0000

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.

$√(2^6) = 2^3 =\huge\boxed{8}$