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

Choose the expression that is equal to the following:

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

Video Solution

Solution Steps

00:07 Let's find expressions that are the same.

00:13 First, write the division as a fraction.

00:16 Divide the root of the numerator called M, by the root of the denominator called N.

00:22 This gives us the root of the fraction, which is M divided by N.

00:27 Now, apply this formula to our exercise.

00:32 And here we have the solution! Great job!

Step-by-Step 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.