To simplify the square root of 30b², extract the square root of the perfect square b² to obtain b outside the radical, and leave the square root of 30 as it is since it has no perfect square factors. The simplified form is b√30.
To simplify the square root of 30b², we want to remove all perfect squares from under the radical. The number 30 can be factored into 3 × 10, and since 10 is 2 × 5, there are no perfect square factors. As for the variable part, b², the exponent 2 indicates that it is a perfect square. Therefore, we can take b out of the square root.
The simplification process is:
Identify perfect square factors: 30 has no perfect squares; b² is a perfect square.
Write the expression as the product of its perfect square and non-perfect square parts: √(30 × b²).
Extract the square root of the perfect square: b.
The square root of 30 remains inside the radical since it cannot be simplified further.
Thus, the simplified form is b√30.