Question

Which expression is equivalent to √175 +2√/28?

OA 9√7
OB. 33√7
OC. 9√5
OD. 7/2

Answer 1

9√7

Explanation:

To simplify the expression
`\(√(175) + 2√(28)\)`, let's break down each square root.

1. For
`\(√(175)\)`, find the prime factorization:

`\[ 175 = 5 * 5 * 7 = 5^2 * 7 \]`

Therefore,
`\(√(175) = √(5^2 * 7) = 5√(7)\)`.

2. For
`\(2√(28)\)`, find the prime factorization:

`\[ 28 = 2 * 2 * 7 = 2^2 * 7 \]`

Therefore,
`\(2√(28) = 2 * 2√(7) = 4√(7)\)`.

Now, substitute these back into the original expression:

`\[ √(175) + 2√(28) = 5√(7) + 4√(7) \]`

Combine like terms:

`\[ = 9√(7) \]`