Question

Simplify. Remove All Perfect Squares From Inside The Square Roots. Assume A And B Are Positive. Square Root Of √81a⁵b=

Answer 1

To simplify the expression √81a⁵b, remove the perfect square from inside the square root, which is 81. Rewrite the expression as 9 * √(a⁵b). The simplified expression is 9a⁵/√b.

Step-by-step explanation:

To simplify the expression √81a⁵b, we can remove the perfect square from inside the square root. In this case, 81 is a perfect square since it can be expressed as 9 * 9. So, we can rewrite the expression as √(9 * 9 * a⁵b). Using the property of square roots that says √(ab) = √a * √b, we can simplify further by taking the square root of the perfect square outside the square root: 9 * √(a⁵b). Finally, we get the simplified expression as 9aⁱ⁄√b.

Answer 2

To simplify √81a⁵b, factor out the perfect square of 81 to get 9, and take out a² as the largest perfect square from a⁵, resulting in the simplified expression 9a²√b.

Step-by-step explanation:

To simplify the expression square root of √81a⁵b, we must identify the perfect squares within the radical and factor them out. The number 81 is a perfect square, since 9 multiplied by 9 equals 81. For the variable portions, we look at the exponents. Since √(a⁵) is a perfect square if 'a' is raised to an even exponent, we can take out 'a' raised to the power of 2 (which is a²) from the radical because a⁵ = a² × a² × a. There is no perfect square for 'b' as its exponent is 1, which is odd.

Step by step, here's how to simplify the expression:

1. Factor out the perfect square of 81: √81 = 9.
2. Factor out the largest perfect square from a⁵, which is a´ (as a² × a²): √a⁵ = √a² × a² × a = a²×√a.
3. There's no perfect square factor for b, so it remains inside the radical.

Putting it all together, the simplified expression is 9a²√b.