Simplify the Square Root Ratio: √a:√b - Step-by-Step Solution

Question

Choose the expression that is equal to the following:

$\sqrt{a}:\sqrt{b}$

00:00 Find equivalent expressions

00:06 Write the division operation as a fraction

00:09 The division of the numerator root (M) by the denominator root (N)

00:12 equals the root of the fraction (M divided by N)

00:15 Apply this formula to our exercise

00:21 This is the solution

To solve the problem, we will apply the rules of roots, specifically the Square Root Quotient Property:

Step 1: The given expression is $\sqrt{a}:\sqrt{b}$ , which represents the division of the square roots.
Step 2: Apply the square root quotient property: $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ .
Step 3: In terms of ratio notation, $\sqrt{a}:\sqrt{b}$ simplifies to $\sqrt{a:b}$ .

Therefore, the expression $\sqrt{a}:\sqrt{b}$ is equivalent to $\sqrt{a:b}$ , which is represented by choice 1.

$\sqrt{a:b}$