一些數學根式問題

2007-09-21 12:53 am
把下列題目簡化/計算下列根式:
1.√2(3√6+4√5)
2.2√a(3√a+5√b)
3.√3(2+√6)-2(√2-√3)
4.√13√30√390
5.√a3√a5√h2
6.4√3(√53+3√3-2√15)
7.(√2+3√6)(6√a+√b)
8.(5√x-2√y)(3√x+4√y)

請給最簡化/最好的答案

回答 (1)

2007-09-21 2:04 am
✔ 最佳答案
1.√2(3√6+4√5)
=3√12 +4 √10
=6√3+4√10

2.2√a(3√a+5√b)
=6a +10√ab

3.√3(2+√6)-2(√2-√3)
=2√3 +3√2 - 2√2 +2√3
=4√3 +√2

4.√13√30√390
=√390 * √390
=390

5.√a3√a5√h2
Do you want to ask a^3, where 3 is the index (指方) of the a?
Suppose it is considered(考慮) as a^3, a^5, h^2
√a^3√a^5√h^2
=√a^8 * h
=a^4 * h

6.4√3(√53+3√3-2√15)
=4√159 + 36 -8√45
=4√159 + 36 -24√5

7.(√2+3√6)(6√a+√b)
=√2(6√a+√b) + 3√6(6√a+√b)
=6√2a +√2b +18√6a + 3√6b
=3√2a(2 + 6√3) + √2b( 1+ 3√3b)

8.(5√x-2√y)(3√x+4√y)
=5√x(3√x+4√y) - 2√y(3√x+4√y)
=15x +20√xy -6√xy -8y
=15x +14√xy -8y
參考: Maths. Knowledge


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