Question

Which calculation correctly uses prism factorization to write the square root of 420 in simplest form?

Answer 1

Answer:

$\sqrt{420}=\sqrt{2\times2\times3\times5\times7} =2\sqrt{105}$

Step-by-step explanation:

We need to write prime factorisation to solve $\sqrt{420}$

Prime factorisation: We need to find only those prime factors that are divisible

So, Prime factors of 420 are: 2x2x3x5x7

Now replacing 420 with its prime factors

$\sqrt{420}\\=\sqrt{2\times2\times3\times5\times7} \\=\sqrt{2^2\times3\times5\times7} \\=\sqrt{2^2}\sqrt{3\times5\times7}\\=2 \sqrt{105}$

Since the options are incomplete, kindly verify the options.

So, $\sqrt{420}=\sqrt{2\times2\times3\times5\times7} =2\sqrt{105}$