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

Video Solution

Solution Steps

00:13 Let's solve this problem together. Here we go!

00:17 First, apply the commutative law to rearrange the numbers.

00:25 When you multiply the square root of A with the square root of B.

00:29 You get the square root of A times B. Easy, right?

00:33 Now, use this formula in our exercise. Let's calculate the product.

00:42 Simplify the expression wherever you can.

00:48 Here, break down nine into three times three.

00:53 Use the formula again and split one root into two.

01:03 Keep simplifying the expression where possible.

01:07 Great job! That's the solution. Well done!

Step-by-Step Solution

Let's proceed to simplify the expression:

First, evaluate the numerator: $\sqrt{2} \cdot \sqrt{9} \cdot \sqrt{2}$ . Using the property $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ , we simplify it: $\sqrt{2 \cdot 9 \cdot 2} = \sqrt{36}$ .
$\sqrt{36}$ simplifies to 6, as 36 is a perfect square.
Next, evaluate the denominator $\sqrt{3} \cdot \sqrt{4}$ :
$\sqrt{3} \cdot \sqrt{4}$ also applies the property $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ , simplifying to $\sqrt{12}$ .
Since 12 is $4 \times 3$ , and $\sqrt{4} = 2$ , $\sqrt{12}$ simplifies to $2\sqrt{3}$ .
Now, the original expression becomes $\frac{6}{2\sqrt{3}}$ .
Simplify $\frac{6}{2}$ to get $\frac{6}{2} = 3$ .
The entire expression now is $\frac{3}{\sqrt{3}}$ .
To rationalize the expression $\frac{3}{\sqrt{3}}$ , multiply both the numerator and the denominator by $\sqrt{3}$ :
This becomes $\frac{3 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}$

Therefore, the solution to the problem is $\sqrt{3}$ .