Multiply and simplify the following radical expressions.
(5√2 − √5)(5√2 − 5√5)
(5√2 − √5)(5√2 − 5√5)
= 50 - 25√10 - 5√10 + 25
collect your like terms and simplify
To multiply and simplify the given radical expressions (5√2 - √5)(5√2 - 5√5), you can use the FOIL method.
FOIL stands for First, Outer, Inner, and Last. It is a method used to multiply two binomials.
First, multiply the first terms of each binomial:
(5√2) * (5√2) = 25 * (√2 * √2) = 25 * 2 = 50.
Outer, multiply the outer terms of each binomial:
(5√2) * (-5√5) = -25 * (√10).
Inner, multiply the inner terms of each binomial:
(-√5) * (5√2) = -25 * (√10).
Last, multiply the last terms of each binomial:
(-√5) * (-5√5) = 25 * 5 = 125.
Combine the results:
50 - 25√10 - 25√10 + 125.
Simplify the like terms:
50 - 50√10 + 125.
Combine the constants:
175 - 50√10.
So, the simplified expression is 175 - 50√10.
To multiply and simplify the given radical expressions, we will use the distributive property.
Step 1: Distribute the first term (5√2) to both terms in the second expression (5√2 − 5√5):
(5√2)(5√2) − (5√2)(5√5)
Step 2: Distribute the second term (−√5) to both terms in the second expression (5√2 − 5√5):
(−√5)(5√2) − (−√5)(5√5)
Step 3: Simplify each multiplication:
(25√4) − (25√10) − (5√10) + (5√25)
Step 4: Simplify the square roots:
(25√4) simplifies to (25 * 2) = 50
√10 cannot be simplified further
−(25√10) simplifies to −(25 * √10)
−√10 cannot be simplified further
(5√25) simplifies to (5 * 5) = 25
Step 5: Combine like terms:
50 − 25√10 − 5√10 + 25
Step 6: Simplify further:
Combine the numbers: 50 + 25 = 75
Combine the square roots: −25√10 − 5√10 = −30√10
Final Answer: 75 − 30√10