Simplify 4/Sqrt98 In 3 Easy Steps

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Simplifying a radical expression like 4/Sqrt98 can seem daunting, but it can be broken down into manageable steps. Here's a simplified guide on how to simplify 4/Sqrt98 in three easy steps.

First, let's understand what Sqrt98 means. Sqrt is short for square root, which is a mathematical operation that finds the number that, when multiplied by itself, gives the original value. For instance, Sqrt16 = 4 because 4 multiplied by 4 equals 16.

Now, let's dive into simplifying 4/Sqrt98.

Step 1: Simplify the Radical

To simplify Sqrt98, we need to find the largest perfect square that divides 98. A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.

98 can be factored as 2 x 49. And 49 is a perfect square, because it's equal to 7 squared (7^2 = 49).

So, we can rewrite Sqrt98 as Sqrt(2 x 49) or Sqrt2 x Sqrt49.

Now, since Sqrt49 is equal to 7, we can simplify further:

Sqrt98 = Sqrt2 x 7

Step 2: Simplify the Fraction

Now that we have simplified the radical, we can rewrite the original expression as:

4/Sqrt98 = 4/(Sqrt2 x 7)

To simplify this fraction, we can multiply both the numerator and the denominator by the square root of 2, which will eliminate the radical in the denominator:

4/(Sqrt2 x 7) = (4 x Sqrt2)/(Sqrt2 x Sqrt2 x 7)

Simplifying further, we get:

(4 x Sqrt2)/(2 x 7) = (4 x Sqrt2)/14

Step 3: Final Simplification

We can simplify the fraction further by dividing both the numerator and the denominator by 2:

(4 x Sqrt2)/14 = (2 x Sqrt2)/7

And that's the simplified form of 4/Sqrt98.

In conclusion, simplifying a radical expression like 4/Sqrt98 requires breaking it down into manageable steps. By simplifying the radical, simplifying the fraction, and performing final simplification, we can arrive at the simplified form of 4/Sqrt98, which is (2 x Sqrt2)/7.

Additional Tips and Tricks:

• Always look for perfect squares when simplifying radicals.
• Multiply and divide fractions by the same value to eliminate radicals in the denominator.
• Simplify fractions by dividing both the numerator and the denominator by common factors.

Actionable Takeaways:

• Practice simplifying radicals with different values.
• Use online resources or calculators to check your work.
• Break down complex problems into manageable steps.

Do you have any questions or need further clarification on simplifying radicals? Share your thoughts in the comments below!