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).