subtract 10√7 - 4√7.
To subtract 10√7 - 4√7, we combine like terms. Since both terms have the same radical (√7), we can subtract their coefficients.
10√7 - 4√7 = (10 - 4)√7 = 6√7
Therefore, 10√7 - 4√7 simplifies to 6√7.
To multiply (-8√21) (-7√2), we multiply the two terms together:
(-8√21) (-7√2) = (-8)(-7)(√21)(√2)
Multiplying the coefficients -8 and -7 gives us 56:
56(√21)(√2)
To simplify further, we can multiply the radicands (√21 and √2):
56(√21)(√2) = 56(√42)
Therefore, (-8√21) (-7√2) simplifies to 56√42.
To multiply (-3√6) (√5), we multiply the two terms together:
(-3√6) (√5) = (-3)(√6)(√5)
Multiplying the coefficients -3 gives us -3:
-3(√6)(√5)
To simplify further, we can multiply the radicands (√6 and √5):
-3(√6)(√5) = -3(√30)
Therefore, (-3√6) (√5) simplifies to -3√30.
To divide 12√15 by 3, we divide the numerical part and divide the radical part separately:
Numerical part: 12/3 = 4
Radical part: √15
Therefore, 12√15/3 simplifies to 4√15.
Multiply (-8√21) (-7√2). Give an exact answer.
Multiply (-3√6) (√5). Give an exact answer.
divide 12√15/3. Provide an exact answer.
Simplify ∛56.
Simplify √170.
responses
a. 17√10
b. 10√17
c. 85
d. This radical expression is already fully simplified.
To simplify ∛56, we need to find the cube root of 56.
The prime factorization of 56 is 2 * 2 * 2 * 7.
Since there is no perfect cube within the prime factors, we cannot simplify ∛56 any further.
Therefore, the simplified form of ∛56 is just ∛56.