Algebra 2B

Unit 2 Sample Work
Radical Functions and Rational Exponents

Simplify the following quotient.

sqrt 8m^5n^6 / sqrt2m^3n^2 • sqrt 6m4^n^4 /sqrt2m^3n^2

sqrt 8m^5n^6 / sqrt2m^3n^2 • sqrt 6m4^n^4 /sqrt2m^3n^2

= √(8m^5 n^6) / √(2m^3 n^2) * √(6m^4 n^4) / √(2m^3 n^2)
= √ [(8m^5 n^6) / (2m^3 n^2) ] * √ [ (6m^4 n^4) / (2m^3 n^2) ]
= √(4m^2 n^4) * √(3m n^2)
= √(12m^3 n^6)
= √12 * √m^3 * √n^6
= 2√3 * m√m * n^3
= 2mn^3 √(3m)

check my steps

sqrt ( 48 m^9 n^10) / 2m^3n^2

( 4 m^4 n^5) sqrt 3 m / 2 m^3 n^2

2 m n^3 sqrt (3m)

oh, good, we agreed

Whew !!

To simplify the given quotient, we can use the properties of radicals and exponents.

Step 1: Simplify each square root individually.

sqrt(8m^5n^6) can be simplified as follows:

sqrt(8) = sqrt(4 * 2) = 2 * sqrt(2)

Now, let's simplify the variables under the square root:

sqrt(m^5n^6) = sqrt(m^4 * m * n^4 * n^2) = m^2n^3

Therefore, sqrt(8m^5n^6) = 2m^2n^3.

Similarly, we can simplify sqrt(6m^4n^4) as follows:

sqrt(6) * sqrt(m^4n^4) = sqrt(6) * m^2n^2

Step 2: Simplify the denominator.

sqrt(2m^3n^2) can be simplified as:

sqrt(2) * sqrt(m^2 * m * n^2) = sqrt(2) * mn * sqrt(m)

Therefore, sqrt(2m^3n^2) = mn * sqrt(2m).

Step 3: Rewrite the quotient.

Now, we can rewrite the given expression with the simplified forms:

(2m^2n^3 / mn * sqrt(2m)) * (sqrt(6) * m^2n^2 / sqrt(2m))

Step 4: Cancel out common factors.

We can cancel out common factors between the numerator and denominator:

2m^2n^3 / mn * sqrt(6) * m^2n^2 / sqrt(2m)

m from mn in the numerator and denominator cancels out.

m^2n from m^2n^3 in the numerator and m^2n^2 in the denominator cancels out.

sqrt(2m) from sqrt(2m) in the numerator and denominator cancels out.

After canceling out the common factors, we are left with:

2n^2 * sqrt(6)

Therefore, the simplified quotient is 2n^2 * sqrt(6).