Solve for X: Simplifying √4·√5/√25 Equation Step-by-Step

Q: Why can't I just multiply the numbers under the square roots first?

You need to follow the order of operations! The expression shows $ \sqrt{4} \cdot \sqrt{5} $, which means multiply the results of each square root, not the numbers inside them.

Q: How do I know when $ \sqrt{5} $ equals $ \frac{\sqrt{20}}{10} $ ?

Use the relationship $ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} $. So $ \frac{\sqrt{20}}{10} = \frac{2\sqrt{5}}{10} = \frac{\sqrt{5}}{5} $. Both forms are equivalent!

Q: Why do I divide both sides by 2 at the end?

Because the equation is $ \frac{2\sqrt{5}}{5} = 2x $. To isolate x, you need to divide both sides by the coefficient 2, giving you $ x = \frac{\sqrt{5}}{5} $.

Q: Can I leave my answer as a decimal instead?

While you could approximate, exact radical form is usually preferred in algebra. $ \frac{\sqrt{20}}{10} $ gives the precise answer, while decimals are approximations.

Q: What's the difference between $ \sqrt{5} $ and $ \sqrt{20} $ ?

$ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} $, so $ \sqrt{20} $ is exactly twice as large as $ \sqrt{5} $. That's why $ \frac{\sqrt{20}}{10} = \frac{\sqrt{5}}{5} $!

Radical Simplification with Fractional Expressions

Solve for x:

$\frac{\sqrt{4}\cdot\sqrt{5}}{\sqrt{25}}=2x$

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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 When multiplying the square root of a number (A) by the square root of another number (B)

00:06 The result equals the square root of their product (A times B)

00:10 Apply this formula to our exercise and proceed to calculate the product

00:15 Let's break down 25 to 5 squared

00:18 Any square root of a number (A) squared equals the number itself (A)

00:25 Apply this formula to our exercise and cancel out the square

00:28 Isolate X

00:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$\frac{\sqrt{4}\cdot\sqrt{5}}{\sqrt{25}}=2x$

Step-by-step solution

To solve $\frac{\sqrt{4} \cdot \sqrt{5}}{\sqrt{25}} = 2x$ , we follow these steps:

Simplify $\sqrt{4}$ : The square root of 4 is 2.
Simplify $\sqrt{5}$ : $\sqrt{5}$ remains $\sqrt{5}$ .
Simplify $\sqrt{25}$ : The square root of 25 is 5.
Substitute these values back: $\frac{2 \cdot \sqrt{5}}{5} = 2x$ .
Write the expression: $\frac{2\sqrt{5}}{5} = 2x$ .
Divide both sides by 2 to solve for $x$ :

x = \frac{2\sqrt{5}}{5 \cdot 2} = \frac{\sqrt{5}}{5}

The simplified expression for $\sqrt{5}$ is equivalent to $\frac{\sqrt{20}}{10}$ , using $\sqrt{5} = \frac{\sqrt{20}}{2}$ since $\sqrt{20} = 2\sqrt{5}$ .

Therefore, the solution to the problem is $\boxed{\frac{\sqrt{20}}{10}}$ .

Final Answer

$x=\frac{\sqrt{20}}{10}$

Key Points to Remember

Essential concepts to master this topic

Simplification: Evaluate each square root separately before combining terms
Technique: $\sqrt{4} = 2$ , $\sqrt{25} = 5$ , then substitute into fraction
Check: Verify $\frac{\sqrt{20}}{10} = \frac{2\sqrt{5}}{10} = \frac{\sqrt{5}}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Combining square roots incorrectly under one radical
Don't write $\sqrt{4 \cdot 5} \div \sqrt{25}$ = wrong simplification! This changes the original expression structure and leads to incorrect results. Always simplify each square root individually first, then perform the arithmetic operations.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

FAQ

Everything you need to know about this question

Why can't I just multiply the numbers under the square roots first?

You need to follow the order of operations! The expression shows $\sqrt{4} \cdot \sqrt{5}$ , which means multiply the results of each square root, not the numbers inside them.

How do I know when $\sqrt{5}$ equals $\frac{\sqrt{20}}{10}$ ?

Use the relationship $\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}$ . So $\frac{\sqrt{20}}{10} = \frac{2\sqrt{5}}{10} = \frac{\sqrt{5}}{5}$ . Both forms are equivalent!

Why do I divide both sides by 2 at the end?

Because the equation is $\frac{2\sqrt{5}}{5} = 2x$ . To isolate x, you need to divide both sides by the coefficient 2, giving you $x = \frac{\sqrt{5}}{5}$ .

Can I leave my answer as a decimal instead?

While you could approximate, exact radical form is usually preferred in algebra. $\frac{\sqrt{20}}{10}$ gives the precise answer, while decimals are approximations.

What's the difference between $\sqrt{5}$ and $\sqrt{20}$ ?

$\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}$ , so $\sqrt{20}$ is exactly twice as large as $\sqrt{5}$ . That's why $\frac{\sqrt{20}}{10} = \frac{\sqrt{5}}{5}$ !

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Solve for X: Simplifying √4·√5/√25 Equation Step-by-Step

Radical Simplification with Fractional Expressions

❤️ 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't I just multiply the numbers under the square roots first?

How do I know when $\sqrt{5}$ equals $\frac{\sqrt{20}}{10}$ ?

Why do I divide both sides by 2 at the end?

Can I leave my answer as a decimal instead?

What's the difference between $\sqrt{5}$ and $\sqrt{20}$ ?

🌟 Unlock Your Math Potential

More Questions

Rules of Roots Combined

Solve for X: Simplifying √20·√5/x = 2√25 Equation

Solve for X: Square Root Equation sqrt(2)·sqrt(4)/sqrt(16) = x/sqrt(8)

Solve for X: Simplifying √8·√4·√2/√2 = √(x²)

Simplify the Square Root Expression: √(12x⁴)

Square Root Quotient Property

Solve the Square Root Equation: Finding X in √6x = √36

Simplify the Expression: (√2 × √9 × √2)/(√3 × √4) Radical Fraction

Solve the Square Root Expression: Simplifying √(2/4)

Solve Square Root: Simplifying √(225/25) Step by Step

Solve for X: Simplifying √4·√5/√25 Equation Step-by-Step

Radical Simplification with Fractional Expressions

❤️ 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't I just multiply the numbers under the square roots first?

How do I know when 5 \sqrt{5} 5​ equals 2010 \frac{\sqrt{20}}{10} 1020​​?

Why do I divide both sides by 2 at the end?

Can I leave my answer as a decimal instead?

What's the difference between 5 \sqrt{5} 5​ and 20 \sqrt{20} 20​?

🌟 Unlock Your Math Potential

More Questions

Rules of Roots Combined

Solve for X: Simplifying √20·√5/x = 2√25 Equation

Solve for X: Square Root Equation sqrt(2)·sqrt(4)/sqrt(16) = x/sqrt(8)

Solve for X: Simplifying √8·√4·√2/√2 = √(x²)

Simplify the Square Root Expression: √(12x⁴)

Square Root Quotient Property

Solve the Square Root Equation: Finding X in √6x = √36

Simplify the Expression: (√2 × √9 × √2)/(√3 × √4) Radical Fraction

Solve the Square Root Expression: Simplifying √(2/4)

Solve Square Root: Simplifying √(225/25) Step by Step

How do I know when $\sqrt{5}$ equals $\frac{\sqrt{20}}{10}$ ?

What's the difference between $\sqrt{5}$ and $\sqrt{20}$ ?