square root of 98 in radical form
Understand the Problem
The question is asking for the square root of 98 expressed in radical form. To solve this, we will simplify the square root expression.
Answer
$7\sqrt{2}$
Answer for screen readers
The simplified form of the square root of 98 is $7\sqrt{2}$.
Steps to Solve
- Factor the number inside the square root
To simplify $\sqrt{98}$, we first want to find its prime factors.
$98 = 2 \times 49$
- Express the factor in square root form
Next, we can see that $49$ is a perfect square. We can express $\sqrt{98}$ as:
$$\sqrt{98} = \sqrt{2 \times 49}$$
- Separate the square root
Now, we can separate the square root into two parts using the property of square roots:
$$\sqrt{98} = \sqrt{2} \times \sqrt{49}$$
- Simplify the perfect square
Since $49$ is a perfect square, we can simplify this further:
$$\sqrt{49} = 7$$
- Final simplification
Now, we can rewrite the equation:
$$\sqrt{98} = 7 \times \sqrt{2}$$
The simplified form of the square root of 98 is $7\sqrt{2}$.
More Information
The square root of 98 simplifies to $7\sqrt{2}$ because 49 is a perfect square, making it easy to simplify the expression. This process is common in algebra when simplifying square roots.
Tips
- Forgetting to factor completely: Sometimes, students may overlook the factors of the number and fail to recognize perfect squares.
- Confusing the $ \sqrt{a \times b} $ property: Not applying the property correctly can lead to incorrect simplifications.
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