what is the square root of 150 in simplified radical form ?
The correct answer and explanation is:
The square root of 150 can be simplified into radical form as follows: 150=25×6\sqrt{150} = \sqrt{25 \times 6}
Since 25 is a perfect square, its square root is 5. Therefore, the expression simplifies to: 150=25×6=56\sqrt{150} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}
Thus, the square root of 150 in simplified radical form is 565\sqrt{6}.
Explanation:
When simplifying square roots, the goal is to factor the number inside the square root into a product of smaller factors, one of which is a perfect square. In this case, the first step is to factor 150 into 25×625 \times 6. The reason we choose 25 is that it is a perfect square, which means its square root can be easily simplified.
Next, we apply the property of square roots: ab=a×b\sqrt{ab} = \sqrt{a} \times \sqrt{b}
This allows us to separate the square root into two parts: 25\sqrt{25} and 6\sqrt{6}. The square root of 25 is 5 because 5×5=255 \times 5 = 25, so the expression simplifies to: 565\sqrt{6}
Since 6 cannot be simplified further (it does not contain any perfect square factors), the expression 565\sqrt{6} is the simplest radical form.
In general, simplifying square roots involves recognizing and factoring perfect squares from the number under the square root. This process helps make the expression more manageable and easier to understand.