Solve: (√4 × √9)/√16 - Square Root Multiplication and Division

Question

Solve the following exercise:

$\frac{\sqrt{4}\cdot\sqrt{9}}{\sqrt{16}}=$

00:00 Solve the following problem

00:03 When multiplying the root of a number (A) by the root of another number (B)

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

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

00:23 The root of any number (A) squared cancels out the square

00:31 Apply this formula to our exercise and cancel out the squares

00:41 Break down 6 into factors of 3 and 2

00:44 Break down 4 into factors of 2 and 2

00:47 This is the solution

To solve this problem, let's carefully follow these steps:

$\sqrt{4} = 2, \quad \sqrt{9} = 3, \quad \sqrt{16} = 4$

The expression in the numerator is $\sqrt{4} \cdot \sqrt{9}$ . Substituting the simplified values, we have:
$2 \cdot 3 = 6$

Now, divide the result from Step 2 by the simplified denominator:
$\frac{6}{4} = \frac{3}{2}$

Thus, the value of the expression is $\frac{3}{2}$ .

Therefore, the solution to the problem is $\frac{3}{2}$ .

$\frac{3}{2}$