Simplify sqrt(98)
Understand the Problem
The question is asking for the simplified form of the square root of 98. To simplify this, we would look for the largest perfect square that divides 98 and factor it out from the square root.
Answer
$7\sqrt{2}$
Answer for screen readers
The simplified form of the square root of 98 is $7\sqrt{2}$.
Steps to Solve
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Identify Perfect Squares We need to find the perfect squares that can factor into 98. The perfect squares less than 98 are 1, 4, 9, 16, 25, 36, 49, and 64. The largest perfect square that divides 98 is 49.
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Factor 98 Next, we can express 98 as a product of 49 and another number: $$ 98 = 49 \times 2 $$
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Apply the Square Root Property Using the property of square roots that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can separate the square root: $$ \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \times \sqrt{2} $$
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Simplify the Square Roots Now, we simplify the square root of 49, which is 7: $$ \sqrt{49} = 7 $$
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Combine the Results Putting it all together, we have: $$ \sqrt{98} = 7 \sqrt{2} $$
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 the largest perfect square less than 98. This highlights the importance of recognizing perfect squares when simplifying square roots.
Tips
- Forgetting to look for the largest perfect square. Always look for the largest perfect square first to simplify the square root effectively.
