Solve the Square Root Equation: √98/√x = 7

Q: Why can I combine the square roots in the fraction?

The property $ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} $ works because division and square roots can be combined when both expressions are under the same radical. This makes the equation easier to solve!

Q: What if x turns out to be negative?

Since we have $ \sqrt{x} $ in the denominator, x must be positive for the equation to be defined. Negative values would make the square root undefined in real numbers.

Q: Do I always need to square both sides with square root equations?

Usually yes, but be careful! Squaring can introduce extraneous solutions, so always check your answer by substituting back into the original equation.

Q: How do I know 98/49 equals 2?

Divide: $ \frac{98}{49} = \frac{2 \times 49}{49} = 2 $. You can also think of it as 98 ÷ 49 = 2 since 49 × 2 = 98.

Q: Can I solve this without combining the square roots?

Yes! You could multiply both sides by $ \sqrt{x} $ first to get $ \sqrt{98} = 7\sqrt{x} $, then square both sides. Both methods work, but combining fractions is usually cleaner.

Square Root Equations with Algebraic Division

$\frac{\sqrt{98}}{\sqrt{x}}=7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the value X

00:03 The square root of the number (A) divided by the square root of the number (B)

00:07 Is the same as the square root of the fraction (A divided by B)

00:10 We'll apply this formula to our exercise and proceed to convert to the root of a fraction

00:16 Square both sides in order to eliminate the fraction

00:26 Squaring cancels out the root

00:29 Calculate 7 squared

00:33 Isolate X

00:51 This is the solution

Step-by-step written solution

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Understand the problem

$\frac{\sqrt{98}}{\sqrt{x}}=7$

Step-by-step solution

To solve this problem, let's proceed with the following steps:

Step 1: Start with the given equation:
$\frac{\sqrt{98}}{\sqrt{x}} = 7$ .
Step 2: Apply the square root property to combine the fraction:
$\sqrt{\frac{98}{x}} = 7$ .
Step 3: Square both sides to eliminate the square root:
$\frac{98}{x} = 49$ .
Step 4: Solve for $x$ by multiplying both sides by $x$ :
$98 = 49x$ .
Step 5: Isolate $x$ by dividing both sides by 49:
$x = \frac{98}{49}$ .
Step 6: Simplify the fraction:
$x = \frac{98}{49} = 2$ .

Therefore, the solution to the problem is $x = 2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Property: $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ for combining square root fractions
Technique: Square both sides to eliminate radicals: $(\sqrt{\frac{98}{x}})^2 = 7^2$
Check: Substitute $x = 2$ back: $\frac{\sqrt{98}}{\sqrt{2}} = 7$ ✓

Common Mistakes

Avoid these frequent errors

Squaring only one side of the equation
Don't square just $\sqrt{\frac{98}{x}}$ and leave 7 unchanged = equation becomes $\frac{98}{x} = 7$ instead of 49! This gives $x = 14$ which is wrong. Always square both sides simultaneously to maintain equality.

Practice Quiz

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Choose the largest value

FAQ

Everything you need to know about this question

Why can I combine the square roots in the fraction?

The property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ works because division and square roots can be combined when both expressions are under the same radical. This makes the equation easier to solve!

What if x turns out to be negative?

Since we have $\sqrt{x}$ in the denominator, x must be positive for the equation to be defined. Negative values would make the square root undefined in real numbers.

Do I always need to square both sides with square root equations?

Usually yes, but be careful! Squaring can introduce extraneous solutions, so always check your answer by substituting back into the original equation.

How do I know 98/49 equals 2?

Divide: $\frac{98}{49} = \frac{2 \times 49}{49} = 2$ . You can also think of it as 98 ÷ 49 = 2 since 49 × 2 = 98.

Can I solve this without combining the square roots?

Yes! You could multiply both sides by $\sqrt{x}$ first to get $\sqrt{98} = 7\sqrt{x}$ , then square both sides. Both methods work, but combining fractions is usually cleaner.

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Solve the Square Root Equation: √98/√x = 7

Square Root Equations with Algebraic Division

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can I combine the square roots in the fraction?

What if x turns out to be negative?

Do I always need to square both sides with square root equations?

How do I know 98/49 equals 2?

Can I solve this without combining the square roots?

🌟 Unlock Your Math Potential

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