First, let's simplify the expressions inside the parentheses:
√32 = √(162) = 4√2√45 = √(95) = 3√5√98 = √(492) = 7√2√72 = √(362) = 6√2√300 = √(1003) = 10√3√8 = √(42) = 2√2
Now substitute the simplified expressions back into the original equation:
(4√2 + 3√5 - 7√2) • (6√2 - 10√3 - 2√2)
Now distribute:
4√2 6√2 = 242 = 484√2 -10√3 = -40√64√2 -2√2 = -8*2 = -16
3√5 6√2 = 18√103√5 -10√3 = -30√153√5 * -2√2 = -6√10
-7√2 6√2 = -422 = -84-7√2 -10√3 = 70√6-7√2 -2√2 = 14
Combine like terms:
48 + (-40√6) + (-16) + 18√10 + (-30√15) + (-6√10) + (-84) + 70√6 + 14
= 46 - 22√6 + 12√10 - 30√15
Therefore, the final answer is 46 - 22√6 + 12√10 - 30√15.
First, let's simplify the expressions inside the parentheses:
√32 = √(162) = 4√2
√45 = √(95) = 3√5
√98 = √(492) = 7√2
√72 = √(362) = 6√2
√300 = √(1003) = 10√3
√8 = √(42) = 2√2
Now substitute the simplified expressions back into the original equation:
(4√2 + 3√5 - 7√2) • (6√2 - 10√3 - 2√2)
Now distribute:
4√2 6√2 = 242 = 48
4√2 -10√3 = -40√6
4√2 -2√2 = -8*2 = -16
3√5 6√2 = 18√10
3√5 -10√3 = -30√15
3√5 * -2√2 = -6√10
-7√2 6√2 = -422 = -84
-7√2 -10√3 = 70√6
-7√2 -2√2 = 14
Combine like terms:
48 + (-40√6) + (-16) + 18√10 + (-30√15) + (-6√10) + (-84) + 70√6 + 14
= 46 - 22√6 + 12√10 - 30√15
Therefore, the final answer is 46 - 22√6 + 12√10 - 30√15.