Simplify \sqrt105

Question

Simplify
`\sqrt`105

Answer 1

Step-by-step explanation:

you are sure ?

sqrt(105)

`√(105)`

105 = 3×35 = 3×5×7

there is no factor that is a square number.

therefore, this cannot be further simplified.

it can be split into parts like

sqrt(3)×sqrt(5)×sqrt(7)

but I would not call that simplified.

we could use exponents :

sqrt(105) = 105^(1/2)

but that's about it.

Answer 2

To simplify the square root of 105, we find the largest perfect square factor of 105, which is 9. Then we simplify further to get 3 times the square root of 11.

Step-by-step explanation:

To simplify √105, we need to find the largest perfect square that is a factor of 105. The largest perfect square factor of 105 is 9 (since 9 is the largest perfect square that is less than 105). Therefore, we can write √105 = √(9 × 11).

Using the property that √(a × b) = √a × √b, we can simplify further: √105 = √9 × √11.

The square root of 9 is 3, so the simplified form of √105 is 3√11.