Question

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


`√(420)`
240 = V2 - 2 - 2 3.5 = 2/30
240 = 2 . 2 . 2 . 2 = 4/3
240 = 2 . 2 . 2 . 2 3.5 4/15
240 V2 · 2 · 2 · 3 3. 10 = 2/60
​

Answer 1

`√(420)=√(2*2*3*5*7) =2√(105)`

Explanation:

We need to write prime factorisation to solve
`√(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

`√(420)\\=√(2*2*3*5*7) \\=√(2^2*3*5*7) \\=√(2^2)√(3*5*7)\\=2 √(105)`

Since the options are incomplete, kindly verify the options.

So,
`√(420)=√(2*2*3*5*7) =2√(105)`