Question

$\sqrt{256 \times 361 }$
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Answer 1

Answer:

$\sqrt{256 * 361} \\\\\\sqrt{16 * 16* 19* 19}$

That would be 16 * 19=304

You can also do prime factorisation in first step

Hope that helped,mark me as brainliest

Answer 2

Method 1

Step 1: Multiply numbers in the square root.

$\sqrt{256\times 361 }$

$\sqrt{92416}$

Step 2: Prime factorize the number.

$\begin{array}{r | l} 2 & 92416\\ \cline{2-2} 2 & 46208 \\ \cline{2-2} 2 & 23104 \\ \cline{2-2} 2 & 11552 \\ \cline{2-2} 2 & 5776\\ \cline{2-2} 2 & 2888 \\ \cline{2-2} 2 & 1444\\ \cline{2-2} 2 & 722 \\ \cline{2-2} 19 & 361 \\ \cline{2-2} & 19 \\\end{array}$

92416 = 2×2×2×2×2×2×2×2×19×19

Step 3: Pair the product of primes.

(2×2)×(2×2)×(2×2)×(2×2)×(19×19)

Step 4: To find the square root take number from each pair and multiply.

$\sqrt{92416} =2\times 2\times 2\times 2\times 19$

$\sqrt{92416} = 304$

$\rule{300}{0.5}$

Method 2

Step 1: Find the square root of 256 through prime factorization.

$\begin{array}{r | l} 2 & 256\\ \cline{2-2} 2 & 128\\ \cline{2-2} 2 & 64 \\ \cline{2-2} 2 & 32 \\ \cline{2-2} 2 & 16\\ \cline{2-2} 2 & 8 \\ \cline{2-2} 2 & 4\\ \cline{2-2} & 2 \\\end{array}$

256 = 2×2×2×2×2×2×2×2

Step 2: Pair the product of primes for 256.

(2×2)×(2×2)×(2×2)×(2×2)

Step 3: To find the square root take number from each pair and multiply.

$\sqrt{256} = 2\times 2\times 2 \times 2$

$\sqrt{256}=16$

Step 4: Find the square root of 361 through prime factorization.

$\begin{array}{r | l} 19 &361 \\ \cline{2-2} & 19\\ \end{array}$

Step 5: Pair the product of primes for 361.

(19×19)

Step 6: To find the square root take number from each pair and multiply.

$\sqrt{361} =19$

Step 7: Multiply both the numbers obtained after finding the square root.

16×19 = 304

$\rule{300}{0.5}$

$\bf \therefore \sqrt{256\times 361 } = 304$